Mathematical game theory and applications
Mazalov, Vladimir
2014-01-01
An authoritative and quantitative approach to modern game theory with applications from diverse areas including economics, political science, military science, and finance. Explores areas which are not covered in current game theory texts, including a thorough examination of zero-sum game.Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games.Explores Bargaining models, discussing new result such as resource distributions, buyer-seller instructions and reputation in bargaining models.Theoretical results are presented along
Economics and Mathematical Theory of Games
Ajda Fosner
2012-01-01
The theory of games is a branch of applied mathematics that is used in economics, management, and other social sciences. Moreover, it is used also in military science, political science, international relations, computer science, evolutionary biology, and ecology. It is a field of mathematics in which games are studied. The aim of this article is to present matrix games and the game theory. After the introduction, we will explain the methodology and give some examples. We will show applicatio...
Mathematical Methods of Game and Economic Theory
Aubin, J-P
1982-01-01
This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself.
Mathematical programming and game theory for decision making
Bapat, R B; Das, A K; Parthasarathy, T
2008-01-01
This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel pro
Mathematical games, abstract games
Neto, Joao Pedro
2013-01-01
User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.
Games, theory and applications
Thomas, L C
2011-01-01
Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to game theory. It opens with the theory of two-person zero-sum games, two-person non-zero sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory books. Succeeding sections focus on a variety of applications - including introductory explanations of gaming and meta games - that offer nonspecialists information about new areas of game theory at a comprehensible level. Numerous exercises appear with full solutions, in addition
de Bruin, B.P.
2005-01-01
Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals
DEFF Research Database (Denmark)
Hendricks, Vincent F.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
Topics in mathematical economics and game theory essays in honor of Robert J. Aumann
Wooders, Myrna H
1999-01-01
Since the publication of Theory of Games and Economic Behavior by von Neumann and Morgenstern, the concept of games has played an increasing role in economics. It also plays a role of growing importance in other sciences, including biology, political science, and psychology. Many scientists have made seminal advances and continue to be leaders in the field, including Harsanyi, Shapley, Shubik, and Selten. Professor Robert Aumann, in addition to his important contributions to game theory and economics, made a number of significant contributions to mathematics. This volume provides a collection
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The basic ideas of game theory were originated from the problems of maximum and minimum given by J.Yon Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems. Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.
Designing and Testing a Mathematics Card Game for Teaching and Learning Elementary Group Theory
Galarza, Patrick
2017-01-01
This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…
Karlin, Anna R
2016-01-01
This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields, such as computer science, economics, social choice, biology, and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. Game theory's influence is felt in a wide range of disciplines, and the authors deliver masterfully on the challenge of presenting both the breadth and coherence of its underlying ...
Dufwenberg, Martin
2011-03-01
Game theory is a toolkit for examining situations where decision makers influence each other. I discuss the nature of game-theoretic analysis, the history of game theory, why game theory is useful for understanding human psychology, and why game theory has played a key role in the recent explosion of interest in the field of behavioral economics. WIREs Cogni Sci 2011 2 167-173 DOI: 10.1002/wcs.119 For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Beasley, John D
2006-01-01
""Mind-exercising and thought-provoking.""-New ScientistIf playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain chance event. This entertaining and wide-ranging guide demonstrates how simple mathematical analysis can throw unexpected light on games of every type-games of chance, games of skill, games of chance and skill, and automatic games.Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strat
Barron, E N
2013-01-01
An exciting new edition of the popular introduction to game theory and its applications The thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models. With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to
Game theory : Noncooperative games
van Damme, E.E.C.; Wright, J.
2015-01-01
We describe noncooperative game models and discuss game theoretic solution concepts. Some applications are also noted. Conventional theory focuses on the question ‘how will rational players play?’, and has the Nash equilibrium at its core. We discuss this concept and its interpretations, as well as
Barron, E N
2008-01-01
A fundamental introduction to modern game theory from a mathematical viewpoint. Game theory arises in almost every fact of human and inhuman interaction since oftentimes during these communications objectives are opposed or cooperation is viewed as an option. From economics and finance to biology and computer science, researchers and practitioners are often put in complex decision-making scenarios, whether they are interacting with each other or working with evolving technology and artificial intelligence. Acknowledging the role of mathematics in making logical and advantageous decisions, Game
Learning Mathematics through Games
Gough, John
2015-01-01
When considering the use of games for teaching mathematics, educators should distinguish between an "activity" and a "game". Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move…
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
Design Principles for Serious Video Games in Mathematics Education: From Theory to Practice
Directory of Open Access Journals (Sweden)
Konstantinos Chorianopoulos
2014-09-01
Full Text Available There is growing interest in the employment of serious video games in science education, but there are no clear design principles. After surveying previous work in serious video game design, we highlighted the following design principles: 1 engage the students with narrative (hero, story, 2 employ familiar gameplay mechanics from popular video games, 3 engage students into constructive trial and error game-play and 4 situate collaborative learning. As illustrated examples we designed two math video games targeted to primary education students. The gameplay of the math video games embeds addition operations in a seamless way, which has been inspired by that of classic platform games. In this way, the students are adding numbers as part of popular gameplay mechanics and as a means to reach the video game objective, rather than as an end in itself. The employment of well-defined principles in the design of math video games should facilitate the evaluation of learning effectiveness by researchers. Moreover, educators can deploy alternative versions of the games in order to engage students with diverse learning styles. For example, some students might be motived and benefited by narrative, while others by collaboration, because it is unlikely that one type of serious video game might fit all learning styles. The proposed principles are not meant to be an exhaustive list, but a starting point for extending the list and applying them in other cases of serious video games beyond mathematics and learning.
Isaacs, Rufus
1999-01-01
Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.
Fujiwara-Greve, Takako
2015-01-01
This is a textbook for university juniors, seniors, and graduate students majoring in economics, applied mathematics, and related fields. Each chapter is structured so that a core concept of that chapter is presented with motivations, useful applications are given, and related advanced topics are discussed for future study. Many helpful exercises at various levels are provided at the end of each chapter. Therefore, this book is most suitable for readers who intend to study non-cooperative game theory rigorously for both theoretical studies and applications. Game theory consists of non-cooperative games and cooperative games. This book covers only non-cooperative games, which are major tools used in current economics and related areas. Non-cooperative game theory aims to provide a mathematical prediction of strategic choices by decision makers (players) in situations of conflicting interest. Through the logical analyses of strategic choices, we obtain a better understanding of social (economic, business) probl...
Reducible and nonsensical uses of game theory
de Bruin, B.P.
The mathematical tools of game theory are frequently used in the social sciences and economic consultancy. But how do they explain social phenomena and support prescriptive judgments? And is the use of game theory really necessary? I analyze the logical form of explanatory and prescriptive game
Mathematics Games with the Alphabet
Gough, John
2004-01-01
Sometimes the first step towards making a new (mathematics) game is discovering an unexpected possibility in some hitherto unplayed-with piece of equipment. At other times the first step is inventing new equipment. But rarely is any "new" idea for a game wholly original, either as a way of playing a game, or in its equipment. As…
Game theory a very short introduction
Binmore, Ken
2007-01-01
Games are played everywhere: from economics and online auctions to social interactions, and game theory is about how to play such games in a rational way, and how to maximize their outcomes. This VSI reveals, without mathematical equations, the insights the theory can bring to everything from how to play poker optimally to the sex ratio among bees. - ;Games are everywhere: Drivers manoeuvring in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. A firm negotiating next year's wage is playing a bargaining game. The opposing candidates in an
Design Principles for Serious Video Games in Mathematics Education: From Theory to Practice
Konstantinos Chorianopoulos; Michail Giannakos
2014-01-01
There is growing interest in the employment of serious video games in science education, but there are no clear design principles. After surveying previous work in serious video game design, we highlighted the following design principles: 1) engage the students with narrative (hero, story), 2) employ familiar gameplay mechanics from popular video games, 3) engage students into constructive trial and error game-play and 4) situate collaborative learning. As illustrated examples we designed two...
DEFF Research Database (Denmark)
Rose, Caspar
2016-01-01
This article shows how game theory can be applied to model good faith mathematically using an example of a classic legal dispute related to rei vindicato. The issue is whether an owner has a legal right to his good if a person has bought it in good faith by using updated probabilities. The article...
The mathematics of games of strategy
Dresher, Melvin
1981-01-01
A noted research mathematician explores decision making in the absence of perfect information. His clear presentation of the mathematical theory of games of strategy encompasses applications to many fields, including economics, military, business, and operations research. No advanced algebra or non-elementary calculus occurs in most of the proofs.
Shor, Mikhael
2003-01-01
States making game theory relevant and accessible to students is challenging. Describes the primary goal of GameTheory.net is to provide interactive teaching tools. Indicates the site strives to unite educators from economics, political and computer science, and ecology by providing a repository of lecture notes and tests for courses using…
Bingo! Select Games for Mathematical Thinking
Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley
2013-01-01
Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…
Dependence theory via game theory
Grossi, D.; Turrini, P.
2011-01-01
In the multi-agent systems community, dependence theory and game theory are often presented as two alternative perspectives on the analysis of social interaction. Up till now no research has been done relating these two approaches. The unification presented provides dependence theory with the sort
Hou, D.; Driessen, Theo
2012-01-01
Inspired by the first lustrum of the Club Positioning Matrix (CPM) for professional Dutch soccer teams, we model the interaction between soccer teams and their potential fans as a cooperative cost game based on the annual voluntary sponsorships of fans in order to validate their fan registration in
Desoer, C. A.; Polak, E.; Zadeh, L. A.
1974-01-01
A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.
Wolpert, David H.
2005-01-01
Probability theory governs the outcome of a game; there is a distribution over mixed strat.'s, not a single "equilibrium". To predict a single mixed strategy must use our loss function (external to the game's players. Provides a quantification of any strategy's rationality. Prove rationality falls as cost of computation rises (for players who have not previously interacted). All extends to games with varying numbers of players.
A Mathematical Model of Game Refinement and Its Applications to Sports Games
Directory of Open Access Journals (Sweden)
Arie Pratama Sutiono
2015-10-01
Full Text Available This paper explores a mathematical model of game progress. We claim that a realistic model of the game progress during the in-game period is not linear but exponential. The second derivative value, i.e., acceleration in the sense of dynamics, is derived from the model and we propose to use the value as a measure of game refinement. T his i s b ecause a cceleration o f g ame p rogress s hould b e r elated t o t he e motional impact i n our minds, as thrill or engagement in games. We also evaluate well known games using our theory like sport games, that would further be classified by the rule to finish the game. It is expected that the game refinement theory will be widely used as a tool to assess the quality of various types of games as a new game theory.
Solving the Sophistication-Population Paradox of Game Refinement Theory
Xiong , Shuo; Tiwary , Parth ,; Iida , Hiroyuki
2016-01-01
Part 4: Short Papers; International audience; A mathematical model of game refinement was proposed based on uncertainty of game outcome. This model has been shown to be useful in measuring the entertainment element in the domains such as boardgames and sport games. However, game refinement theory has not been able to explain the correlation between the popularity of a game and the game refinement value. This paper introduces another aspect in the study of game entertainment, the concept of “a...
DEFF Research Database (Denmark)
Aarseth, Espen
2012-01-01
In this article I present a narrative theory of games, building on standard narra-tology, as a solution to the conundrum that has haunted computer game studies from the start: How to approach software that combines games and stories?......In this article I present a narrative theory of games, building on standard narra-tology, as a solution to the conundrum that has haunted computer game studies from the start: How to approach software that combines games and stories?...
Rapoport, Anatol
1999-01-01
Clear, accessible treatment of mathematical models for resolving conflicts in politics, economics, war, business, and social relationships. Topics include strategy, game tree and game matrix, and much more. Minimal math background required. 1970 edition.
Game Design and Development as Mathematical Activities
DEFF Research Database (Denmark)
Jensen, Erik Ottar; Hanghøj, Thorkild; Misfeldt, Morten
2016-01-01
education which have mostly been tied to students making learning games involving specific mathematical content. Game design activities are reported to have a motivational pull for students. A challenge seems to be that the students are mostly motivated by the game design or the programming activities...... between user and goal through the computational artifacts being used. The framework serves as a lens for making sense of computer game design as a context for learning mathematics....
Game theory a nontechnical introduction
Davis, Morton D
1997-01-01
""A lucid and penetrating development of game theory that will appeal to the intuition . . . a most valuable contribution."" - Douglas R. Hofstadter Fascinating, accessible introduction to enormously important intellectual system with numerous applications to social, economic, political problems. Newly revised edition offers overview of game theory, then lucid coverage of the two-person zero-sum game with equilibrium points; the general, two-person zero-sum game; utility theory; other topics. Problems at start of each chapter.
The Chess and Mathematics Connection: More than Just a Game
Berkman, Robert M.
2004-01-01
This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…
Directory of Open Access Journals (Sweden)
Romeu Costa Ribeiro Bastos
2011-06-01
Full Text Available The processes of regional integration has aroused great interest in the field of International Relations since the 1950s, however, there has been renovated enthusiasm especially in the 1980s, in view of the successful experience of European Union and the creation of Mercosur. This article aims at analyzing the positions of Brazil and Argentina within Mercosur, using the instruments supplied by the Game Theory.
van Damme, E.E.C.
1995-01-01
This paper surveys some recent developments in (non-cooperative) game theory and provides an outlook on the near future of that theory. In particular, attention is focused on the limitations inherent in normative game theory and on attempts to construct a behavioral version of the theory that
Computer-Game-Based Tutoring of Mathematics
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
International Nuclear Information System (INIS)
Agrachev, A.A.
2002-01-01
This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, robotics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume
Energy Technology Data Exchange (ETDEWEB)
Agrachev, A A [Steklov Mathematical Institute, Moscow (Russian Federation); SISSA, Trieste [Italy; ed.
2002-07-15
This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, tics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume contains
Evolutionary game theory and organizational ecology: The case of resource-partitioning theory
ZHOU, Chaohong; VAN WITTELOOSTUIJN, Arjen
2009-01-01
Abstract: In this paper, we construct a mathematical model that applies tools from evolutionary game theory to issues in organizational ecology. Evolutionary game theory shares the key feature of mathematical rigor with the industrial organization tradition, but is similar to organizational ecology by emphasizing evolutionary dynamics. Evolutionary game theory may well be a complementary modeling tool for the analytical study of organizational ecology issues, next to formal logic, standard ga...
Using Game Theory Techniques and Concepts to Develop Proprietary Models for Use in Intelligent Games
Christopher, Timothy Van
2011-01-01
This work is about analyzing games as models of systems. The goal is to understand the techniques that have been used by game designers in the past, and to compare them to the study of mathematical game theory. Through the study of a system or concept a model often emerges that can effectively educate students about making intelligent decisions…
Studies in the Theory of Quantum Games
Iqbal, Azhar
2005-03-01
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.
Toward an Analysis of Video Games for Mathematics Education
Offenholley, Kathleen
2011-01-01
Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…
McCain, Roger A
2015-01-01
This book provides a critical, selective review of concepts from game theory and their applications in public policy, and further suggests some modifications for some of the models (chiefly in cooperative game theory) to improve their applicability to economics and public policy.
Stohler, Michael Lehman
2002-01-01
Non-cooperative quantum games have received much attention recently. This thesis defines and divides current works into two major categories of gaming techniques with close attention paid to Nash equilibria, form and possibilities for the payoff functions, and the benefits of using a quantum strategy. In addition to comparing and contrasting these techniques, new applications and calculations are discussed. Finally, the techniques are expanded into 3 x 3 games which allows the study of non-transitive strategies in quantum games.
Foundations of game theory noncooperative games
Vorob’ev, Nicolai N
1994-01-01
The English edition differs only slightly from the Russian original. The main struc tural difference is that all the material on the theory of finite noncooperative games has been collected in Chapter 2, with renumbering of the material of the remain ing chapters. New sections have been added in this chapter: devoted to general questions of equilibrium theory in nondegenerate games, subsections 3.9-3.17, by N.N. Vorob'ev, Jr.; and § 4, by A.G. Chernyakov; and § 5, by N.N. Vorob'ev, Jr., on the computational complexity of the process of finding equilibrium points in finite games. It should also be mentioned that subsections 3.12-3.14 in Chapter 1 were written by E.B. Yanovskaya especially for the Russian edition. The author regrets that the present edition does not reflect the important game-theoretical achievements presented in the splendid monographs by E. van Damme (on the refinement of equilibrium principles for finite games), as well as those by J.e. Harsanyi and R. Selten, and by W. Giith and B. Ka...
Mathematical History: Activities, Puzzles, Stories, and Games.
Mitchell, Merle
Based on the history of mathematics, these materials have been planned to enrich the teaching of mathematics in grades four, five, and six. Puzzles and games are based on stories about topics such as famous mathematicians, numerals of ancient peoples, and numerology. The sheets are arranged by grade level and are designed for easy duplication.…
Game theory and experimental games the study of strategic interaction
Colman, Andrew M
1982-01-01
Game Theory and Experimental Games: The Study of Strategic Interaction is a critical survey of the essential ideas of game theory and the findings of empirical research on strategic interaction. Some experiments using lifelike simulations of familiar kinds of strategic interactions are presented, and applications of game theory to the study of voting, the theory of evolution, and moral philosophy are discussed.Comprised of 13 chapters, this volume begins with an informal definition of game theory and an outline of the types of social situations to which it applies. Games of skill, games of cha
The Uses of Teaching Games in Game Theory Classes and Some Experimental Games.
Shubik, Martin
2002-01-01
Discusses the use of lightly controlled games, primarily in classes in game theory. Considers the value of such games from the viewpoint of both teaching and experimentation and discusses context; control; pros and cons of games in teaching; experimental games; and games in class, including cooperative game theory. (Author/LRW)
Dixit, Avinash
2005-01-01
The author suggests methods for teaching game theory at an introductory level, using interactive games to be played in the classroom or in computer clusters, clips from movies to be screened and discussed, and excerpts from novels and historical books to be read and discussed.
Introduction: games and subcultural theory
Directory of Open Access Journals (Sweden)
Marco Benoit Carbone
2014-03-01
Full Text Available This issue of GAME Journal offers a recognition and a series of case studies on video games from the point of view of subcultural theory. Game studies have hitherto focused little on their object from this perspective, which offers a theoretical frame for the historical and ever growing complexity of the audiences involved with the medium of the video game. The study of subcultures on the other hand has a long standing and complex tradition which culminates in what has been recently defined as the “post-subcultural” theoretical scenario.
DEFF Research Database (Denmark)
Jensen, Frank; Frost, Hans Staby; Thøgersen, Thomas Talund
2015-01-01
of the mackerel crisis is based on a statistical estimation of relevant functional relations, and the behavior of the players is explained using a fully specified empirical model. Simple, non-cooperative game theory shows that all players have an incentive to act non-cooperatively, a result that is robust......Simple non-cooperative and cooperative game theory is used to explore the crisis involving the European Union (EU), Norway, Iceland and the Faroe Islands regarding the size and relative allocation of total allowable catches (TACs) in the mackerel fishery in the Northeast Atlantic. The analysis...... to changes in basic assumptions regarding demand and cost functions. Thus, using the estimated parameters and functions, simple, non-cooperative game theory cannot explain the cooperative behavior of EU and Norway during the mackerel crisis. Simple cooperative game theory shows that no player has...
Game theory decisions, interaction and evolution
Webb, James N
2007-01-01
This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics. The outstanding feature of the book is that it provides a unified account of three types of decision problem: Situations involving a single decision-maker: in which a sequence of choices is to be made in "a game against nature". This introduces the basic ideas of optimality and decision processes. Classical game theory: in which the interactions of two or more decision-makers are considered. This leads to the concept of the Nash equilibrium. Evolutionary game theory: in which the changing structure of a population of interacting decision makers is considered. This leads to the ideas of evolutionarily stable strategies and replicator dynamics. An understanding of basic calculus and probability is assumed but no prior knowledge of gam...
Models in cooperative game theory
Branzei, Rodica; Tijs, Stef
2008-01-01
This book investigates models in cooperative game theory in which the players have the possibility to cooperate partially. In a crisp game the agents are either fully involved or not involved at all in cooperation with some other agents, while in a fuzzy game players are allowed to cooperate with infinite many different participation levels, varying from non-cooperation to full cooperation. A multi-choice game describes the intermediate case in which each player may have a fixed number of activity levels. Different set and one-point solution concepts for these games are presented. The properties of these solution concepts and their interrelations on several classes of crisp, fuzzy, and multi-choice games are studied. Applications of the investigated models to many economic situations are indicated as well. The second edition is highly enlarged and contains new results and additional sections in the different chapters as well as one new chapter.
Introduction to the theory of games
McKinsey, John C C
1952-01-01
One of the classic early monographs on game theory, this comprehensive overview illustrates the theory's applications to situations involving conflicts of interest, including economic, social, political, and military contexts. Contents include a survey of rectangular games; a method of approximating the value of a game; games in extensive form and those with infinite strategies; distribution functions; Stieltjes integrals; the fundamental theorem for continuous games; separable games; games with convex payoff functions; applications to statistical inference; and much more. Appropriate for adva
Game theory and plant ecology.
McNickle, Gordon G; Dybzinski, Ray
2013-04-01
The fixed and plastic traits possessed by a plant, which may be collectively thought of as its strategy, are commonly modelled as density-independent adaptations to its environment. However, plant strategies may also represent density- or frequency-dependent adaptations to the strategies used by neighbours. Game theory provides the tools to characterise such density- and frequency-dependent interactions. Here, we review the contributions of game theory to plant ecology. After briefly reviewing game theory from the perspective of plant ecology, we divide our review into three sections. First, game theoretical models of allocation to shoots and roots often predict investment in those organs beyond what would be optimal in the absence of competition. Second, game theoretical models of enemy defence suggest that an individual's investment in defence is not only a means of reducing its own tissue damage but also a means of deflecting enemies onto competitors. Finally, game theoretical models of trade with mutualistic partners suggest that the optimal trade may reflect competition for access to mutualistic partners among plants. In short, our review provides an accessible entrance to game theory that will help plant ecologists enrich their research with its worldview and existing predictions. © 2013 Blackwell Publishing Ltd/CNRS.
N-person game theory concepts and applications
Rapoport, Anatol
2013-01-01
N-person game theory provides a logical framework for analyzing contests in which there are more than two players or sets of conflicting interests-anything from a hand of poker to the tangled web of international relations. In this sequel to his Two-Person Game Theory, Dr. Rapoport provides a fascinating and lucid introduction to the theory, geared towards readers with little mathematical background but with an appetite for rigorous analysis.Following an introduction to the necessary mathematical notation (mainly set theory), in Part I the author presents basic concepts and models, including
Games Superheroes Play: Teaching Game Theory with Comic Book Favorites
O'Roark, Brian; Grant, William
2018-01-01
The valuable insights of game theory sometimes remain out of reach for students who are overwhelmed by the subject's complexity. Comic book applications of game theory, with superheroes as players, can facilitate enthusiasm and classroom interaction to enhance the learning of game theory. Drawing from content in superhero movies and books, the…
Mathematical programming in multiperson cooperative games
Energy Technology Data Exchange (ETDEWEB)
Lucas, W.
1994-12-31
Many fundamental solution notions in mathematical economics relate to mathematical programming. This includes various types of equilibrium points for the noncooperative (strategic) competitions, as well as the core for the cooperative (coalitional) models. This talk concerns alternate cooperative solution concepts such as various nucleoli points and other proposed fairness outcomes. These concepts become of particular interest for those cases when the core is an empty set. Recent results on these alternate solutions for classes of assignment games will be presented.
Game theory, social choice and ethics
1979-01-01
There are problems to whose solution I would attach an infinitely greater import ancf! than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not...
CERN. Geneva
2014-01-01
This lecture series will present the main directions of Algorithmic Game Theory, a new field that has emerged in the last two decades at the interface of Game Theory and Computer Science, because of the unprecedented growth in size, complexity, and impact of the Internet and the Web. These include the price of anarchy (what is the impact of selfishness on a system of competing entities), computational complexity (can the market find a reasonable solution), mechanisms and auctions (what incentives to give to selfish individuals).
CERN. Geneva
2014-01-01
This lecture series will present the main directions of Algorithmic Game Theory, a new field that has emerged in the last two decades at the interface of Game Theory and Computer Science, because of the unprecedented growth in size, complexity, and impact of the Internet and the Web. These include the price of anarchy (what is the impact of selfishness on a system of competing entities), computational complexity (can the market find a reasonable solution), mechanisms and auctions (what incentives to give to selfish individuals).
Essentials of Game Theory A Concise Multidisciplinary Introduction
Leyton-Brown, Kevin
2008-01-01
Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthes
Mathematical Modeling of Language Games
Loreto, Vittorio; Baronchelli, Andrea; Puglisi, Andrea
In this chapter we explore several language games of increasing complexity. We first consider the so-called Naming Game, possibly the simplest example of the complex processes leading progressively to the establishment of human-like languages. In this framework, a globally shared vocabulary emerges as a result of local adjustments of individual word-meaning association. The emergence of a common vocabulary only represents a first stage while it is interesting to investigate the emergence of higher forms of agreement, e.g., compositionality, categories, syntactic or grammatical structures. As an example in this direction we consider the so-called Category Game. Here one focuses on the process by which a population of individuals manages to categorize a single perceptually continuous channel. The problem of the emergence of a discrete shared set of categories out of a continuous perceptual channel is a notoriously difficult problem relevant for color categorization, vowels formation, etc. The central result here is the emergence of a hierarchical category structure made of two distinct levels: a basic layer, responsible for fine discrimination of the environment, and a shared linguistic layer that groups together perceptions to guarantee communicative success.
Evolutionary Game Theory and Leadership
Guastello, Stephen J.
2009-01-01
Comments on the article Leadership, followership, and evolution: Some lessons from the past by Van Vugt, Hogan, and Kaiser. This article offers a fresh perspective on leaders, followers, and their possible origins in nonhuman and primitive human behavior patterns. The connections between group coordination, leadership, and game theory have some…
Ethics, Morality, and Game Theory
Directory of Open Access Journals (Sweden)
Mark Alfano
2018-04-01
Full Text Available Ethics is a field in which the gap between words and actions looms large. Game theory and the empirical methods it inspires look at behavior instead of the lip service people sometimes pay to norms. We believe that this special issue comprises several illustrations of the fruitful application of this approach to ethics.
Potential game theory applications in radio resource allocation
Lã, Quang Duy; Soong, Boon-Hee
2016-01-01
This book offers a thorough examination of potential game theory and its applications in radio resource management for wireless communications systems and networking. The book addresses two major research goals: how to identify a given game as a potential game, and how to design the utility functions and the potential functions with certain special properties in order to formulate a potential game. After proposing a unifying mathematical framework for the identification of potential games, the text surveys existing applications of this technique within wireless communications and networking problems found in OFDMA 3G/4G/WiFi networks, as well as next-generation systems such as cognitive radios and dynamic spectrum access networks. Professionals interested in understanding the theoretical aspect of this specialized field will find Potential Game Theory a valuable resource, as will advanced-level engineering students. It paves the way for extensive and rigorous research exploration on a topic whose capacity for...
Arfi, Badredine
2007-02-01
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large- N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.
Digital games and learning mathematics: Student, teacher and parent perspectives
Su Ting Yong; Peter Gates; Ian Harrison
2016-01-01
The purpose of this study was to explore the potential use of digital games in learning mathematics at secondary school level in Malaysia. Three secondary school students, three mathematics teachers and three parents were interviewed in this study. All the participants were asked for their views and experiences in mathematics, technology usage and the use of digital games in learning mathematics. The results suggested that students were supportive and positive towards the use of computer game...
Student-Made Games to Learn the History of Mathematics
Huntley, Mary Ann; Flores, Alfinio
2011-01-01
In this article, the authors describe how prospective secondary mathematics teachers designed their own adaptations of popular board and computer games to learn the history of mathematics. They begin the article by describing some of the games students designed and used, and follow this with a discussion of factors for successful use of games in…
National Research Council Canada - National Science Library
Washburn, Alan
2000-01-01
.... Nothing could be further from the truth. In fact, the authors hoped that their theory might form the basis of decision making in all situations where multiple decision makers can affect an outcome, a large class of situations that includes...
Rational Density Functional Selection Using Game Theory.
McAnanama-Brereton, Suzanne; Waller, Mark P
2018-01-22
Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.
Game theory, conditional preferences, and social influence.
Stirling, Wynn C; Felin, Teppo
2013-01-01
Neoclassical noncooperative game theory is based on a simple, yet powerful synthesis of mathematical and logical concepts: unconditional and immutable preference orderings and individual rationality. Although this structure has proven useful for characterizing competitive multi-player behavior, its applicability to scenarios involving complex social relationships is problematic. In this paper we directly address this limitation by the introduction of a conditional preference structure that permits players to modulate their preference orderings as functions of the preferences of other players. Embedding this expanded preference structure in a formal and graphical framework provides a systematic approach for characterizing a complex society. The result is an influence network that allows conditional preferences to propagate through the community, resulting in an emergent social model which characterizes all of the social relationships that exist and which leads to solution concepts that account for both group and individual interests. The Ultimatum game is presented as an example of how social influence can be modeled with conditional preferences.
Networks and learning in game theory
Kets, W.
2008-01-01
This work concentrates on two topics, networks and game theory, and learning in games. The first part of this thesis looks at network games and the role of incomplete information in such games. It is assumed that players are located on a network and interact with their neighbors in the network.
Why Darwin would have loved evolutionary game theory.
Brown, Joel S
2016-09-14
Humans have marvelled at the fit of form and function, the way organisms' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin's arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so. © 2016 The Author(s).
ter Vrugte, Judith; de Jong, Anthonius J.M.; Vandercruysse, Sylke; Wouters, Pieter; van Oostendorp, Herre; Elen, Jan
2015-01-01
The present study addresses the effectiveness of an educational mathematics game for improving proportional reasoning in students from prevocational education. Though in theory game-based learning is promising, research shows that results are ambiguous and that we should look into ways to support
The Effects of an Educational Video Game on Mathematical Engagement
Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Deater-Deckard, Kirby; Samur, Yavuz
2016-01-01
In an effort to maximizing success in mathematics, our research team implemented an educational video game in fifth grade mathematics classrooms in five schools in the Eastern US. The educational game was developed by our multi-disciplinary research team to achieve a hypothetical learning trajectory of mathematical thinking of 5th grade students.…
Game Engagement Theory and Adult Learning
Whitton, Nicola
2011-01-01
One of the benefits of computer game-based learning is the ability of certain types of game to engage and motivate learners. However, theories of learning and engagement, particularly in the sphere of higher education, typically fail to consider gaming engagement theory. In this article, the author examines the principles of engagement from games…
Games in the mathematics curriculum: Some conceptions and ...
African Journals Online (AJOL)
Games in the mathematics curriculum: Some conceptions and experiences of teachers in the Upper West Region of Ghana. ... The study investigated primary school teachers' experiences with games as ... AJOL African Journals Online.
Using Student-Made Games to Learn Mathematics
Gallegos, Irene; Flores, Alfinio
2010-01-01
First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)
Quantum Uncertainty and Decision-Making in Game Theory
Asano, M.; Ohya, M.; Tanaka, Y.; Khrennikov, A.; Basieva, I.
2011-01-01
Recently a few authors pointed to a possibility to apply the mathematical formalism of quantum mechanics to cognitive psychology, in particular, to games of the Prisoners Dilemma (PD) type.6_18 In this paper, we discuss the problem of rationality in game theory and point out that the quantum uncertainty is similar to the uncertainty of knowledge, which a player feels subjectively in his decision-making.
Evolutionary Game Theory: A Renaissance
Directory of Open Access Journals (Sweden)
Jonathan Newton
2018-05-01
Full Text Available Economic agents are not always rational or farsighted and can make decisions according to simple behavioral rules that vary according to situation and can be studied using the tools of evolutionary game theory. Furthermore, such behavioral rules are themselves subject to evolutionary forces. Paying particular attention to the work of young researchers, this essay surveys the progress made over the last decade towards understanding these phenomena, and discusses open research topics of importance to economics and the broader social sciences.
Yu.S. Osipov's work in mathematical control theory
International Nuclear Information System (INIS)
Kryazhimskiy, Arkady A
2006-01-01
This paper gives an overview of Yu.S. Osipov's work in mathematical control theory, including development of the theory of positional differential games for control systems with time delay; analysis of the phenomenon of infinite dimensionality of the state space of a dynamical system in the context of differential games; development of the theory of dynamical inversion (dynamical regularization) for finite- and infinite-dimensional control systems; applications of methods of the theory of positional differential games beyond the scope of the theory itself; work on new differential-game methods and on methods of control under incomplete information. The author of this overview is the first student of Osipov, and also his longstanding colleague.
Using Digital Games to Learn Mathematics – What students think?
Su Ting Yong; Ian Harrison; Peter Gates
2016-01-01
The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study. The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games. It was found that most of the university foundation students liked to play different types of digital games. ...
Matemáticas y juego = Mathematics and games
Alsina, Angel
2001-01-01
In this article we try to look at the learning of mathematics through games in the first years of schooling. The use of game resources in the class should not be carried out in a uniquely intuitive way but rather in a manner that contains some preliminary reflections such as, what do we understand by games? Why use games as a resource in the Mathematics classroom? And what does its use imply?
Decision and game theory in management with intuitionistic fuzzy sets
Li, Deng-Feng
2014-01-01
The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to us...
Explaining games the epistemic programme in game theory
de Bruin, Boudewijn
2010-01-01
The first monograph on the philosophy of game theory, this is a bold attempt to combine insights from epistemic logic and the philosophy of science to assess the applicability of game theory in such fields as economics, philosophy and strategic consultancy.
A quest towards a mathematical theory of living systems
Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine
2017-01-01
This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three...
Game Theory in the Social Studies Classroom
Vesperman, Dean Patrick; Clark, Chris H.
2016-01-01
This article explores using game theory in social studies classrooms as a heuristic to aid students in understanding strategic decision making. The authors provide examples of several simple games teachers can use. Next, we address how to help students design their own simple (2 × 2) games.
Case Study of an Epistemic Mathematics Computer Game
Buteau, Chantal; Muller, Eric
2018-01-01
E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical…
Implementing a Game for Supporting Learning in Mathematics
Katmada, Aikaterini; Mavridis, Apostolos; Tsiatsos, Thrasyvoulos
2014-01-01
This paper focuses on the design, implementation and evaluation of an online game for elementary and middle school mathematics. Its aim is twofold: (a) the development of the prototype of a flexible and adaptable computer game, and (b) the evaluation of this prototype, as to its usability and technical aspects. The particular computer game was…
Effects of Game Technology on Elementary Student Learning in Mathematics
Shin, Namsoo; Sutherland, LeeAnn M.; Norris, Cathleen A.; Soloway, Elliot
2012-01-01
This paper reports the effects of game technology on student learning in mathematics as investigated in two data sets collected from slightly different subjects. In the first, 41 second graders (7 or 8 years old) from two classes used either a technology-based game or a paper-based game for 5 weeks. For the next 13 weeks, both classes used a…
Mathematical game type optimization of powerful fast reactors
International Nuclear Information System (INIS)
Pavelesku, M.; Dumitresku, Kh.; Adam, S.
1975-01-01
To obtain maximum speed of putting into operation fast breeders it is recommended on the initial stage of putting into operation these reactors to apply lower power which needs less fission materials. That is why there is an attempt to find a configuration of a high-power reactor providing maximum power for minimum mass of fission material. This problem has a structure of the mathematical game with two partners of non-zero-order total and is solved by means of specific aids of theory of games. Optimal distribution of fission and breeding materials in a multizone reactor first is determined by solution of competitive game and then, on its base, by solution of the cooperation game. The second problem the solution for which is searched is developed from remark on the fact that a reactor with minimum coefficient of flux heterogenity has a configuration different from the reactor with power coefficient heterogenity. Maximum burn-up of fuel needs minimum heterogenity of the flux coefficient and the highest power level needs minimum coefficient of power heterogenity. That is why it is possible to put a problem of finding of the reactor configuration having both coefficients with minimum value. This problem has a structure of a mathematical game with two partners of non-zero-order total and is solved analogously giving optimal distribution of fuel from the new point of view. In the report is shown that both these solutions are independent which is a result of the aim put in the problem of optimization. (author)
Game theory in communication networks cooperative resolution of interactive networking scenarios
Antoniou, Josephina
2012-01-01
A mathematical tool for scientists and researchers who work with computer and communication networks, Game Theory in Communication Networks: Cooperative Resolution of Interactive Networking Scenarios addresses the question of how to promote cooperative behavior in interactive situations between heterogeneous entities in communication networking scenarios. It explores network design and management from a theoretical perspective, using game theory and graph theory to analyze strategic situations and demonstrate profitable behaviors of the cooperative entities. The book promotes the use of Game T
Kovalenkov, Alexander; Wooders, Myrna Holtz
2002-01-01
In a series of papers (Kovalenkov and Wooders 2001a, Games and Economic Behavior, 2001b, Mathematics of Operations Research, and 1997, Journal of Economic Theory to appear), the authors have developed the framework of parameterized collections of games and also that of parameterized collections of economies with clubs. These papers apply to collections of games with nontransferable utility and similarly to economies with clubs and general preferences. The game theoretic framework encompasses ...
Online game-enhanced teaching in game theory
Badeau-Mahmoud, Sonia; Deloche, Regis; Koscielniak, Thierry
2014-01-01
Introducing digital educational games into class lessons can generate engagement, interactivity, and motivation. It can also result in an active participation of the students in the classroom. To achieve this goal, one teaching strategy is to use online digital games in teaching and learning situations. In our case, we wanted to test this strategy in an economics course, especially in a Game Theory lesson. We set up an experiment in two different lessons: the “Economie expérimentale” (...
Games, Game Flow, and Gender as They Affect Mathematics Achievement of Pupils in Nigeria
Directory of Open Access Journals (Sweden)
A. Aremu
2016-08-01
Full Text Available Game flow experience in the use of games has the potential of determining whether games used for learning would achieve the desired goal of improved achievement. With a subject like Mathematics, it is vital to ensure that if game based strategies are to be used, the games must possess this very important construct. Furthermore, the games must be able to produce the flow experience in both males and females, so that the observed gender gap in the learning of the subject would not be further widened. It is therefore important to investigate the gender differences in a game based learning environment for a subject such as Mathematics. This is the purpose of this research. This research investigated games, game flow, and gender as they affect Mathematics achievement of pupils in Nigeria. Through the use of Achievement of Pupils in Fraction-concepts Test (APFT and Game Flow Questionnaire (GFQ, data were collected. The result was a significant difference in mathematics achievements of pupils exposed to game based strategy and those exposed to modified conventional method of teaching. However, there was no significant difference in game flow experiences, as well as in mathematics achievement of male and female pupils exposed to game based strategy.
Mathematical foundations of transport theory
International Nuclear Information System (INIS)
Ershov, Yu.I.; Shikhov, S.B.
1985-01-01
Main items of application of the operator equations analyzing method in transport theory problems are considered. The mathematical theory of a reactor critical state is presented. Theorems of existence of positive solutions of non-linear non-stationary equations taking into account the temperature and xenon feedbacks are proved. Conditions for stability and asymptotic stability of steady-state regimes for different distributed models of a nuclear reactor are obtained on the basis of the modern operator perturbation theory, certain problems on control using an absorber are considered
Mathematical methods of electromagnetic theory
Friedrichs, Kurt O
2014-01-01
This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in el
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
Nunokawa, Kazuhiko
1996-01-01
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
The mathematical foundations of gauge theories
International Nuclear Information System (INIS)
Marathe, K.B.; Martucci, G.
1992-01-01
Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures. Gauge Theory is such a gift from physics to mathematics. This book presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. (author). refs.; figs.; tabs
Li, Jing; Ma, Sujuan; Ma, Linqing
Firstly, in this article, we expound the theory of the educational games and multiple intelligence and analyze the relationship between them. Then, further, we elaborate educational games' effect on the development of students' multiple intelligence, taking logic-mathematics intelligence for example. Also, we discuss the strategies of using educational games to improve students' intelligence. In a word, we can use the computer games to develop the students' multi-intelligence.
Using Digital Games to Learn Mathematics – What students think?
Directory of Open Access Journals (Sweden)
Su Ting Yong
2016-06-01
Full Text Available The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study. The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games. It was found that most of the university foundation students liked to play different types of digital games. Males preferred playing digital games in more traditional male genres namely sport, racing, shooter, action adventure, role play and strategy games. As for females, they generally preferred playing puzzle and simulation games. Astonishingly, the foundation students were not very positive towards the use of digital games in learning mathematics, and their attitude was essentially influenced by their mathematics interest. Students with greater interest in mathematics were more likely to support the use of digital games in learning.
Game theory and its applications in the social and biological sciences
Colman, Andrew M; Humphreys, Peter; Negrine, Ralph
2013-01-01
Andrew Coleman provides an accessible introduction to the fundamentals of mathematical gaming and other major applications in social psychology, decision theory, economics, politics, evolutionary biology, philosophy, operational research and sociology.
Mathematical theory of sedimentation analysis
Fujita, Hiroshi; Van Rysselberghe, P
1962-01-01
Mathematical Theory of Sedimentation Analysis presents the flow equations for the ultracentrifuge. This book is organized into two parts encompassing six chapters that evaluate the systems of reacting components, the differential equations for the ultracentrifuge, and the case of negligible diffusion. The first chapters consider the Archibald method for molecular weight determination; pressure-dependent sedimentation; expressions for the refractive index and its gradient; relation between refractive index and concentration; and the analysis of Gaussian distribution. Other chapters deal with th
Mathematical foundations of transport theory
International Nuclear Information System (INIS)
Ershov, Yu.I.; Shikhov, S.B.
1985-01-01
Foundations of mathematical transport theory are presented. Definitions and theorems of functional analysis are given. Linear kinetic equation of neutron transport in multiplication media is derived. A model of neutron interaction with nuclei of medium determining completely the coefficient properties in transport equation is described. Non-stationary problems regarding and without regard of d=e layed neutrons are analyzed. Results of solving Cauchy problem are discussed
Effects of mathematical game and instructional analogy as advance ...
African Journals Online (AJOL)
The study investigated the effects of mathematical game and instructional analogy on students' achievement in junior secondary school mathematics. A total of 246 Junior Secondary Two (JS2) Mathematics students were involved in the study. A 3×2 factorial design was adopted in the research. From the findings, it was ...
Computational Aspects of Cooperative Game Theory
Chalkiadakis, Georgios; Wooldridge, Michael
2011-01-01
Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representation
What If Quantum Theory Violates All Mathematics?
Rosinger, Elemér Elad
2017-09-01
It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.
Evolutionary quantum game theory in the context of socio-economic systems
International Nuclear Information System (INIS)
Hanauske, Matthias
2011-01-01
The evolution of socio-economic systems depend on the interdependent decision processes of its underlying system components. The mathematical model to describe the strategic decision of players within a socio-economic game is ''game theory''. ''Quantum game theory'' is a mathematical and conceptual amplification of classical game theory. The space of all conceivable decision paths is extended from the purely rational, measurable space in the Hilbert-space of complex numbers - which is the mathematical space where quantum theory is formulated. By the concept of a potential entanglement of the imaginary quantum strategy parts, it is possible to include cooperate decision path, caused by cultural or moral standards. If this strategy entanglement is large enough, then additional Nash equilibria can occur, previously present dominant strategies could become nonexistent and new evolutionary stable strategies do appear for some game classes. Within this PhD thesis the main results of classical and quantum games are summarized and all of the possible game classes of evolutionary (2 player)-(2 strategy) games are extended to quantum games. It is shown that the quantum extension of classical games with an underlying dilemma-like structure give different results, if the strength of strategic entanglement is above a certain barrier. After the German summary and the introduction paper, five different applications of the theory are discussed within the thesis. (orig.)
The Effects of Modern Mathematics Computer Games on Mathematics Achievement and Class Motivation
Kebritchi, Mansureh; Hirumi, Atsusi; Bai, Haiyan
2010-01-01
This study examined the effects of a computer game on students' mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skill, and English language skill on their achievement and motivation as they played the game. A total of 193 students and 10 teachers participated in this study. The teachers were randomly…
Digital games and learning mathematics: Student, teacher and parent perspectives
Directory of Open Access Journals (Sweden)
Su Ting Yong
2016-12-01
Full Text Available The purpose of this study was to explore the potential use of digital games in learning mathematics at secondary school level in Malaysia. Three secondary school students, three mathematics teachers and three parents were interviewed in this study. All the participants were asked for their views and experiences in mathematics, technology usage and the use of digital games in learning mathematics. The results suggested that students were supportive and positive towards the use of computer games in learning mathematics. Nevertheless, parents preferred conventional teaching approach, in which they recognized personal communication and socialization as a significant component in learning. Although the teachers did not go on to oppose the idea of using computer games for teaching mathematics, they still perceived the use of discursive approaches as the best teaching approach for learning mathematics with digital technologies at best a possible additional complementary feature. In view of that, the combination of classroom teaching and computer games might the best mathematics pedagogy.
Traffic Games: Modeling Freeway Traffic with Game Theory.
Cortés-Berrueco, Luis E; Gershenson, Carlos; Stephens, Christopher R
2016-01-01
We apply game theory to a vehicular traffic model to study the effect of driver strategies on traffic flow. The resulting model inherits the realistic dynamics achieved by a two-lane traffic model and aims to incorporate phenomena caused by driver-driver interactions. To achieve this goal, a game-theoretic description of driver interaction was developed. This game-theoretic formalization allows one to model different lane-changing behaviors and to keep track of mobility performance. We simulate the evolution of cooperation, traffic flow, and mobility performance for different modeled behaviors. The analysis of these results indicates a mobility optimization process achieved by drivers' interactions.
Evolutionary Game Theory Analysis of Tumor Progression
Wu, Amy; Liao, David; Sturm, James; Austin, Robert
2014-03-01
Evolutionary game theory applied to two interacting cell populations can yield quantitative prediction of the future densities of the two cell populations based on the initial interaction terms. We will discuss how in a complex ecology that evolutionary game theory successfully predicts the future densities of strains of stromal and cancer cells (multiple myeloma), and discuss the possible clinical use of such analysis for predicting cancer progression. Supported by the National Science Foundation and the National Cancer Institute.
Gender Differences in Students' Mathematics Game Playing
Lowrie, Tom; Jorgensen, Robyn
2011-01-01
The investigation monitored the digital game-playing behaviours of 428 primary-aged students (aged 10-12 years). Chi-square analysis revealed that boys tend to spend more time playing digital games than girls while boys and girls play quite different game genres. Subsequent analysis revealed statistically significant gender differences in terms of…
Gaming mindsets: implicit theories in serious game learning.
Lee, Yu-Hao; Heeter, Carrie; Magerko, Brian; Medler, Ben
2012-04-01
Individuals' beliefs about the malleability of their abilities may predict their response and outcome in learning from serious games. Individuals with growth mindsets believe their abilities can develop with practice and effort, whereas individuals with fixed mindsets believe their abilities are static and cannot improve. This study uses survey and gameplay server data to examine the implicit theory of intelligence in the context of serious game learning. The findings show that growth mindset players performed better than fixed mindset players, their mistakes did not affect their attention to the game, and they read more learning feedback than fixed mindset players. In addition, growth mindset players were more likely to actively seek difficult challenges, which is often essential to self-directed learning. General mindset measurements and domain-specific measurements were also compared. These findings suggest that players' psychological attributes should be considered when designing and applying serious games.
Effectiveness of Using Games in Tertiary-Level Mathematics Classrooms
Afari, Ernest; Aldridge, Jill M.; Fraser, Barry J.
2012-01-01
The primary focus of this study was to investigate the effectiveness of games when used in tertiary-level mathematics classes in the United Arab Emirates. Our study incorporated a mixed-method approach that involved surveys (to assess students' perceptions of the learning environment and attitudes towards mathematics), interviews, observations of…
Friedman, Avner
2006-01-01
This volume lays the mathematical foundations for the theory of differential games, developing a rigorous mathematical framework with existence theorems. It begins with a precise definition of a differential game and advances to considerations of games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, and games with restricted phase coordinates. Final chapters cover selected topics (including capturability and games with delayed information) and N-person games.Geared toward graduate students, Differential Games will be of particular interest
Game Theory for Wireless Sensor Networks: A Survey
Shi, Hai-Yan; Wang, Wan-Liang; Kwok, Ngai-Ming; Chen, Sheng-Yong
2012-01-01
Game theory (GT) is a mathematical method that describes the phenomenon of conflict and cooperation between intelligent rational decision-makers. In particular, the theory has been proven very useful in the design of wireless sensor networks (WSNs). This article surveys the recent developments and findings of GT, its applications in WSNs, and provides the community a general view of this vibrant research area. We first introduce the typical formulation of GT in the WSN application domain. The roles of GT are described that include routing protocol design, topology control, power control and energy saving, packet forwarding, data collection, spectrum allocation, bandwidth allocation, quality of service control, coverage optimization, WSN security, and other sensor management tasks. Then, three variations of game theory are described, namely, the cooperative, non-cooperative, and repeated schemes. Finally, existing problems and future trends are identified for researchers and engineers in the field. PMID:23012533
Game Theory for Wireless Sensor Networks: A Survey
Directory of Open Access Journals (Sweden)
Ngai-Ming Kwok
2012-07-01
Full Text Available Game theory (GT is a mathematical method that describes the phenomenon of conflict and cooperation between intelligent rational decision-makers. In particular, the theory has been proven very useful in the design of wireless sensor networks (WSNs. This article surveys the recent developments and findings of GT, its applications in WSNs, and provides the community a general view of this vibrant research area. We first introduce the typical formulation of GT in the WSN application domain. The roles of GT are described that include routing protocol design, topology control, power control and energy saving, packet forwarding, data collection, spectrum allocation, bandwidth allocation, quality of service control, coverage optimization, WSN security, and other sensor management tasks. Then, three variations of game theory are described, namely, the cooperative, non-cooperative, and repeated schemes. Finally, existing problems and future trends are identified for researchers and engineers in the field.
Game theory and its applications
Matsumoto, Akio
2015-01-01
This book integrates the fundamentals, methodology and major application fields of noncooperative and cooperative games, including conflict resolution. It includes a wide range of applications in many different areas, from economics to homeland security.
Dynamic games theory and applications
Haurie, Alain
2005-01-01
Dynamic games continue to attract strong interest from researchers interested in modeling competitive and conflict situations to study the behavior of players (decision-makers) and to predict the outcome of such situations in many areas including engineering, economics, management science, military, biology, and political science. This collection of articles by established researchers is an excellent reference covering a wide range of emerging and revisited problems in both cooperative and non-cooperative games.
Quantum information theory mathematical foundation
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...
Game theory and power theory : a critical comparison
Balzer, Wolfgang
1992-01-01
Social actions can be formulated in the frame of game theory or in a frame using, and foccussing on, the notion of power. The two frames are described and clarified. The comparison of theories from these two branches are evaluated from the point of theory of science.
Evolutionary game theory: molecules as players.
Bohl, Katrin; Hummert, Sabine; Werner, Sarah; Basanta, David; Deutsch, Andreas; Schuster, Stefan; Theissen, Günter; Schroeter, Anja
2014-12-01
In this and an accompanying paper we review the use of game theoretical concepts in cell biology and molecular biology. This review focuses on the subcellular level by considering viruses, genes, and molecules as players. We discuss in which way catalytic RNA can be treated by game theory. Moreover, genes can compete for success in replication and can have different strategies in interactions with other genetic elements. Also transposable elements, or "jumping genes", can act as players because they usually bear different traits or strategies. Viruses compete in the case of co-infecting a host cell. Proteins interact in a game theoretical sense when forming heterodimers. Finally, we describe how the Shapley value can be applied to enzymes in metabolic pathways. We show that game theory can be successfully applied to describe and analyse scenarios at the molecular level resulting in counterintuitive conclusions.
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Attribution models and the Cooperative Game Theory
Cano Berlanga, Sebastian; Vilella, Cori
2017-01-01
The current paper studies the attribution model used by Google Analytics. Precisely, we use the Cooperative Game Theory to propose a fair distribution of the revenues among the considered channels, in order to facilitate the cooperation and to guarantee stability. We define a transferable utility convex cooperative game from the observed frequencies and we use the Shapley value to allocate the revenues among the di erent channels. Furthermore, we evaluate the impact of an advertising...
Mathematical theories of distributed sensor networks
Iyengar, Sitharama S; Balakrishnan, N
2014-01-01
Mathematical Theory of Distributed Sensor Networks demonstrates how mathematical theories can be used to provide distributed sensor modeling and to solve important problems such as coverage hole detection and repair. The book introduces the mathematical and computational structure by discussing what they are, their applications and how they differ from traditional systems. The text also explains how mathematics are utilized to provide efficient techniques implementing effective coverage, deployment, transmission, data processing, signal processing, and data protection within distributed sensor networks. Finally, the authors discuss some important challenges facing mathematics to get more incite to the multidisciplinary area of distributed sensor networks.
Group decisions in biodiversity conservation: implications from game theory.
Frank, David M; Sarkar, Sahotra
2010-05-27
Decision analysis and game theory have proved useful tools in various biodiversity conservation planning and modeling contexts. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto-inefficient Nash equilibria. These are cases in which each agent pursuing individual self-interest leads to a worse outcome for all, relative to other feasible outcomes. Three case studies from biodiversity conservation contexts showing this feature are modeled to demonstrate how game-theoretical representation can inform group decision-making. The mathematical theory of games is used to model three biodiversity conservation scenarios with Pareto-inefficient Nash equilibria: (i) a two-agent case involving wild dogs in South Africa; (ii) a three-agent raptor and grouse conservation scenario from the United Kingdom; and (iii) an n-agent fish and coral conservation scenario from the Philippines. In each case there is reason to believe that traditional mechanism-design solutions that appeal to material incentives may be inadequate, and the game-theoretical analysis recommends a resumption of further deliberation between agents and the initiation of trust--and confidence--building measures. Game theory can and should be used as a normative tool in biodiversity conservation contexts: identifying scenarios with Pareto-inefficient Nash equilibria enables constructive action in order to achieve (closer to) optimal conservation outcomes, whether by policy solutions based on mechanism design or otherwise. However, there is mounting evidence that formal mechanism-design solutions may backfire in certain cases. Such scenarios demand a return to group deliberation and the creation of reciprocal relationships of trust.
Group decisions in biodiversity conservation: implications from game theory.
Directory of Open Access Journals (Sweden)
David M Frank
Full Text Available BACKGROUND: Decision analysis and game theory have proved useful tools in various biodiversity conservation planning and modeling contexts. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto-inefficient Nash equilibria. These are cases in which each agent pursuing individual self-interest leads to a worse outcome for all, relative to other feasible outcomes. Three case studies from biodiversity conservation contexts showing this feature are modeled to demonstrate how game-theoretical representation can inform group decision-making. METHODOLOGY AND PRINCIPAL FINDINGS: The mathematical theory of games is used to model three biodiversity conservation scenarios with Pareto-inefficient Nash equilibria: (i a two-agent case involving wild dogs in South Africa; (ii a three-agent raptor and grouse conservation scenario from the United Kingdom; and (iii an n-agent fish and coral conservation scenario from the Philippines. In each case there is reason to believe that traditional mechanism-design solutions that appeal to material incentives may be inadequate, and the game-theoretical analysis recommends a resumption of further deliberation between agents and the initiation of trust--and confidence--building measures. CONCLUSIONS AND SIGNIFICANCE: Game theory can and should be used as a normative tool in biodiversity conservation contexts: identifying scenarios with Pareto-inefficient Nash equilibria enables constructive action in order to achieve (closer to optimal conservation outcomes, whether by policy solutions based on mechanism design or otherwise. However, there is mounting evidence that formal mechanism-design solutions may backfire in certain cases. Such scenarios demand a return to group deliberation and the creation of reciprocal relationships of trust.
European Conference on Game Theory & Networking Games and Management
Mazalov, Vladimir
2016-01-01
This contributed volume contains fourteen papers based on selected presentations from the European Conference on Game Theory SING11-GTM 2015, held at Saint Petersburg State University in July 2015, and the Networking Games and Management workshop, held at the Karelian Research Centre of the Russian Academy of Sciences in Petrozvavodsk, Russia, also in July 2015. These papers cover a wide range of topics in game theory, including recent advances in areas with high potential for future work, as well as new developments on classical results. Some of these include A new approach to journal ranking using methods from social choice theory; A differential game of a duopoly in which two firms are competing for market share in an industry with network externalities; The impact of information propagation in the model of tax audits; A voting model in which the results of previous votes can affect the process of coalition formation in a decision-making body; The Selten-Szidarovsky technique for the analysis of Nash equil...
Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics
Wolpert, David H.
2005-01-01
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.
What If Quantum Theory Violates All Mathematics?
Directory of Open Access Journals (Sweden)
Rosinger Elemér Elad
2017-09-01
Full Text Available It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on …
Active Learning with Monty Hall in a Game Theory Class
Brokaw, Alan J.; Merz, Thomas E.
2004-01-01
The authors describe a game that students can play on the first day of a game theory class. The game introduces the 4 essential elements of any game and is designed so that its sequel, also played on the first day of class, has students playing the well-known Monty Hall game, which raises the question: Should you switch doors? By implementing a…
Game Theory in Wireless Ad-Hoc Opportunistic Radios
Mumtaz, Shahid; Gameiro, Atilio
2010-01-01
Emerging research in game theory based power control applied to ad hoc opportunist networks shows much promise to help understand the complex interactions between OR nodes in this highly dynamic and distributed environment. Also, the employment of game theory in modeling dynamic situations for opportunist ad hoc networks where OR nodes have incomplete information has led to the application of largely unexplored games such as games of imperfect monitoring. Ad hoc security using game theory is ...
Essays in game theory and natural resource management
Pham Do, K.H.
2003-01-01
This thesis presents a collection of essays in game theory with applications to environmental resource problems and their management. A major focus of these essays is related to coalitional games in which several classes of games, their properties and solution concepts are studied. Game theory is
the roles of games in teaching and learning of mathematics in junior ...
African Journals Online (AJOL)
users
The research seeks to enhance the status of games in teaching mathematics in ... that the use of games and activities can make the mathematics enjoyable. ... motivation, understanding and suppression of anxiety are some of the reasons ...
The roles of games in teaching and learning of mathematics in junior ...
African Journals Online (AJOL)
The roles of games in teaching and learning of mathematics in junior secondary schools. ... The research seeks to enhance the status of games in teaching mathematics in junior secondary schools curriculum ... AJOL African Journals Online.
Game theory and strategy in medical training.
Blake, Amy; Carroll, Bryan T
2016-11-01
This paper analyses how game theory can provide a framework for understanding the strategic decision-making that occurs in everyday scenarios in medical training and practice, and ultimately serves as a tool for improving the work environment and patient care. Game theory has been applied to a variety of fields outside of its native economics, but has not been thoroughly studied in the context of health care provision. The paper discusses four of the most common 'games' and applies each to a scenario in medicine to provide new insight on the incentives and drivers for certain types of behaviour and a deeper understanding of why certain results are valued more strongly than others. Using game theory as an integrative tool, in conjunction with good judgement and a sound knowledge base, trainees and physicians can work to better recognise where competing priorities exist, understand the motivations and interactions of the various players, and learn to adjust their approaches in order to 'change the game' when their preferred outcome is not the most likely one. © 2016 John Wiley & Sons Ltd and The Association for the Study of Medical Education.
Game Theory: An Application to Tanners and 'Pomo' Wholesalers in ...
African Journals Online (AJOL)
Game Theory: An Application to Tanners and 'Pomo' Wholesalers in Hides Marketing Competition in Nigeria. ... Agricultural economics is an applied social science so game theory was applied practically from a ... AJOL African Journals Online.
Formulated linear programming problems from game theory and its ...
African Journals Online (AJOL)
Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.
On the Relevance of Game Theory in Strategic Thinking ...
African Journals Online (AJOL)
On the Relevance of Game Theory in Strategic Thinking. ... The author reviews some of the applicable literature and shows how game theory can be used to predict the outcome of a strategy, explain why a ... AJOL African Journals Online.
Game Theory and its Relationship with Linear Programming Models ...
African Journals Online (AJOL)
Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.
Zero-determinant strategy: An underway revolution in game theory
International Nuclear Information System (INIS)
Hao Dong; Rong Zhi-Hai; Zhou Tao
2014-01-01
Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions according to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant (ZD) strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two players, indicating that a smart player can control her unwitting co-player's payoff in a unilateral way [Proc. Acad. Natl. Sci. USA 109, 10409 (2012)]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players, and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis, cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed. (topical review - statistical physics and complex systems)
Evolutionary game theory: cells as players.
Hummert, Sabine; Bohl, Katrin; Basanta, David; Deutsch, Andreas; Werner, Sarah; Theissen, Günter; Schroeter, Anja; Schuster, Stefan
2014-12-01
In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.
Contributions to Pursuit-Evasion Game Theory
Oyler, Dave Wilson
is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.
Directory of Open Access Journals (Sweden)
Reginaldo Santana Figueiredo
1994-12-01
Full Text Available O presente trabalho tem por objetivo a sistematização e a apresentação dos conceitos fundamentais da Teoria dos Jogos, a formalização matemática dos principais conceitos clássicos de solução de um jogo e ilustrar sua aplicação ao problema da distribuição de custo conjunto. Como produto de uma pesquisa de alguns anos, conseguimos reunir sistematicamente o conjunto de conceitos de solução de jogos donde se derivam todos conceitos encontrados nos textos atuais. Apresentamos os conceitos de solução para os chamados jogos cooperativos através do conceito de objeção e contra-objeção de forma a mostrar que os mesmos podem ser vistos como um processo de negociação.This paper presents the basic concepts of Game Theory and the mathematical formalizations of classic concepts of game solutions. We surveyed the fundamental concepts from where we derive the concepts of game solutions that can be found in the modern papers. We feature the concepts to the game named cooperative-games by concepts of objection and counterobjection to show that they can be understood as a negotiation process. In addition, we show how the Game Theory can be applied to the problem of the assignment of joint cost.
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Embedding Diagnostic Mechanisms in a Digital Game for Learning Mathematics
Huang, Yueh-Min; Huang, Shu-Hsien; Wu, Ting-Ting
2014-01-01
Mathematics is closely related to daily life, but it is also one of the lessons which often cause anxiety to primary school students. Digital game-based learning (DGBL) has been regarded as a sound learning strategy in raising learner willingness and interest in many disciplines. Thus, ways of designing a DGBL system to mitigate anxiety are well…
Differential Effects of Learning Games on Mathematics Proficiency
Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Samur, Yavuz
2015-01-01
This study examined the effects of a learning game, [The Math App] on the mathematics proficiency of middle school students. For the study, researchers recruited 306 students, Grades 6-8, from two schools in rural southwest Virginia. Over a nine-week period, [The Math App] was deployed as an intervention for investigation. Students were assigned…
Classroom Proven Motivational Mathematics Games, Monograph No. 1.
Michigan Council of Teachers of Mathematics.
This collection includes 50 mathematical games and puzzles for classroom use at all grade levels. Also included is a wide variety of activities with cubes, flash cards, graphs, dots, number patterns, geometric shapes, cross-number puzzles, and magic squares. (MM)
Game Development as Students’ Engagement Project in High School Mathematics
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Ryan V. Dio
2015-12-01
Full Text Available The general expectancies of the enhanced basic education curriculum in the Philippines focuses on the performance standards which can be expressed when students are able to produce products as evidence that they can transfer or use their learning in real-life situations. One way to assess students achievement is through an engaging activities that would require them apply the knowledge and skills acquired in the subject as the outcome of their learning. This descriptive method of research employed content analysis procedures and survey in describing and assessing the significant feature of the mathematical games as potential learning devices developed by the high school students through an engaging task assignment. It utilized purposive sampling techniques in the selection of the respondents and the submitted write-ups of mathematical games for analysis as typical sample in this study. The study revealed that the high school students developed mathematical board games with different objectives and mechanics as inspired by their learning, experiences, hobbies, and interest. Mathematical concepts and processes along numbers and number sense, measurements, algebra, geometry, and probability and statistics were integrated in the game through question card and mechanics of the game itself. The groups of students and teachers have high level of agreement as to the workmanship and usability, mechanics and organization, relevance to instruction/learning, and fun and enjoyment of the game as revealed by their assessment from very satisfactory to excellent level. Results implied that teachers in any subject area may use students’ engagement project as teaching strategy to produce products and performance that would provide evidence of students’ learning. The school curriculum makers may consider the students’ output as subjects of research for further improvements, exhibits, and classroom utilization.
Enhancing Mathematical Communication: "Bag of Tricks" Game
Patahuddin, Sitti Maesuri; Ramful, Ajay; Greenlees, Jane
2015-01-01
An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.
Mathematical aspects of quantum field theory
de Faria, Edson
2010-01-01
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Evolutionary game theory and criticality
Mahmoodi, Korosh; Grigolini, Paolo
2017-01-01
We study a regular two-dimensional network of individuals playing the Prisonner’s Dilemma game with their neighbors, assigning to each individual the adoption of two different criteria to make a choice between cooperation and defection. For a fraction q incentive to cheat yields the extinction of cooperation and a modest one leads to the survival of cooperation. We show that for K={{K}\\text{c}} the adoption of a very small value of ɛ exerts a bias in favor of either cooperation or defection, as a form of criticality-induced intelligence, which leads the system to select either the cooperation or the defection branch, when K>{{K}\\text{c}} . Intermediate values of ɛ annihilated criticality-induced cognition and, as consequence, may favor defection choice even in the case when a wise payoff consideration is expected to yield the emergence of cooperation.
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Mathematical theory of peer-instruction dynamics
Directory of Open Access Journals (Sweden)
Hideo Nitta
2010-08-01
Full Text Available A mathematical theory of peer instruction describing the increase of the normalized number of correct answers due to peer discussion is presented. A simple analytic expression is derived which agrees with class data. It is shown that our theory is connected to the mathematical learning models proposed by Pritchard et al. It is also shown that obtained theoretical lines are useful for analyzing peer-instruction efficiencies.
Using experimental game theory to transit human values to ethical AI
Wang, Yijia; Wan, Yan; Wang, Zhijian
2017-01-01
Knowing the reflection of game theory and ethics, we develop a mathematical representation to bridge the gap between the concepts in moral philosophy (e.g., Kantian and Utilitarian) and AI ethics industry technology standard (e.g., IEEE P7000 standard series for Ethical AI). As an application, we demonstrate how human value can be obtained from the experimental game theory (e.g., trust game experiment) so as to build an ethical AI. Moreover, an approach to test the ethics (rightness or wrongn...
Econophysics: from Game Theory and Information Theory to Quantum Mechanics
Jimenez, Edward; Moya, Douglas
2005-03-01
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory.
Some Links Between Game Theory and Decision Theory in Economics
Dominika Crnjac; Goran Martinovic
2009-01-01
Certain optimal strategies based upon game theory are given in this paper. A decision-making function and a risk function are explained. Decision-making criteria are applied for determining best decision-making functions with respect to a specific criterion. Special attention is given to the minimax criterion.
Building counting by traditional game: Mathematics Program for Young Children
Nasrullah Nasrullah; Zulkardi Zulkardi
2011-01-01
In line with design research, the use of Bermain Satu Rumah (BSR) as traditional game to support children’s counting classroom wherein students are encouraged to construct mathematical understanding. Number in traditional games is an interesting aspect that is helpful for children to encounter numerous situations that bring them into contact with sounds, symbols and meanings that relate to numbers. Bermain satu rumah as starting activity would be media to enhance student’s sense of number as...
An Analysis of Stochastic Game Theory for Multiagent Reinforcement Learning
National Research Council Canada - National Science Library
Bowling, Michael
2000-01-01
.... In this paper we contribute a comprehensive presentation of the relevant techniques for solving stochastic games from both the game theory community and reinforcement learning communities. We examine the assumptions and limitations of these algorithms, and identify similarities between these algorithms, single agent reinforcement learners, and basic game theory techniques.
Complex adaptive systems and game theory: An unlikely union
Hadzikadic, M.; Carmichael, T.; Curtin, C.
2010-01-01
A Complex Adaptive System is a collection of autonomous, heterogeneous agents, whose behavior is defined with a limited number of rules. A Game Theory is a mathematical construct that assumes a small number of rational players who have a limited number of actions or strategies available to them. The CAS method has the potential to alleviate some of the shortcomings of GT. On the other hand, CAS researchers are always looking for a realistic way to define interactions among agents. GT offers an attractive option for defining the rules of such interactions in a way that is both potentially consistent with observed real-world behavior and subject to mathematical interpretation. This article reports on the results of an effort to build a CAS system that utilizes GT for determining the actions of individual agents. ?? 2009 Wiley Periodicals, Inc. Complexity, 16,24-42, 2010.
Evolutionary game theory using agent-based methods.
Adami, Christoph; Schossau, Jory; Hintze, Arend
2016-12-01
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Pre-Game-Theory Based Information Technology (GAMBIT) Study
National Research Council Canada - National Science Library
Polk, Charles
2003-01-01
.... The generic GAMBIT scenario has been characterized as Dynamic Hierarchical Gaming (DHG). Game theory is not yet ready to fully support analysis of DHG, though existing partial analysis suggests that a full treatment is practical in the midterm...
Evidence Combination From an Evolutionary Game Theory Perspective.
Deng, Xinyang; Han, Deqiang; Dezert, Jean; Deng, Yong; Shyr, Yu
2016-09-01
Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempster's rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solution's stability and convergence, have been mathematically proved as well.
The Effects of Computer Games on the Achievement of Basic Mathematical Skills
Sayan, Hamiyet
2015-01-01
This study aims to analyze the relationship between playing computer games and learning basic mathematics skills. It shows the role computer games play in the learning and achievement of basic mathematical skills by students. Nowadays it is clear that individuals, especially young persons are very fond of computer and computer games. Since…
Impact of Online Flexible Games on Students' Attitude towards Mathematics
Mavridis, Apostolos; Katmada, Aikaterini; Tsiatsos, Thrasyvoulos
2017-01-01
This study examined the effects of using an online flexible educational game on students' attitude towards mathematics as compared to the traditional method of solving mathematical problems. Moreover, the study assessed the learning effectiveness of the game and investigated potential gender differences in the game's effectiveness on changing…
Spatial mathematics theory and practice through mapping
Arlinghaus, Sandra Lach
2013-01-01
In terms of statistics, GIS offers many connections. With GIS, data are gathered, displayed, summarized, examined, and interpreted to discover patterns. Spatial Mathematics: Theory and Practice through Mapping uses GIS as a platform to teach mathematical concepts and skills through visualization of numbers. It examines theory and practice from disparate academic disciplines such as geography, mathematics, physics, and general social science. This approach allows students to grapple with biodiversity, crime, natural hazards, climate, energy, water, and other relevant real-world issues of the twenty-first century. Includes QR Codes Linked to Animated Maps, a Mapping Activity Site, or to an Interactive Webpage, Creating an Interactive Resource That Stays Relevant The book integrates competing philosophical views of the world: synthesis and analysis. These two approaches yield different results and employ different tools. This book considers both approaches to looking at real-world issues that have mathematics as...
Mathematical and physical theory of turbulence
Cannon, John
2006-01-01
Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...
Type classes for mathematics in type theory
Spitters, Bas; Van der Weegen, Eelis
2011-01-01
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage of their unique features to make practical a particularly flexible approach formerly thought infeasible. Thus, we address both traditional proof engineering challenges as well as new ones resulting from our ambition to build upon this development a library...
General systems theory mathematical foundations
Mesarovic, Mihajlo D
1975-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Digital Game-Based Learning for K-12 Mathematics Education: A Meta-Analysis
Byun, JaeHwan; Joung, Eunmi
2018-01-01
Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta-analysis study (a) investigates the current trend of digital game-based learning (DGBL) by reviewing the research studies on the use of DGBL for…
Using game theory to improve safety within chemical industrial parks
Reniers, Genserik
2013-01-01
Though the game-theoretic approach has been vastly studied and utilized in relation to economics of industrial organizations, it has hardly been used to tackle safety management in multi-plant chemical industrial settings. Using Game Theory for Improving Safety within Chemical Industrial Parks presents an in-depth discussion of game-theoretic modelling which may be applied to improve cross-company prevention and -safety management in a chemical industrial park. By systematically analyzing game-theoretic models and approaches in relation to managing safety in chemical industrial parks, Using Game Theory for Improving Safety within Chemical Industrial Parks explores the ways game theory can predict the outcome of complex strategic investment decision making processes involving several adjacent chemical plants. A number of game-theoretic decision models are discussed to provide strategic tools for decision-making situations. Offering clear and straightforward explanations of methodologies, Using Game Theor...
Economic game theory for mutualism and cooperation.
Archetti, Marco; Scheuring, István; Hoffman, Moshe; Frederickson, Megan E; Pierce, Naomi E; Yu, Douglas W
2011-12-01
We review recent work at the interface of economic game theory and evolutionary biology that provides new insights into the evolution of partner choice, host sanctions, partner fidelity feedback and public goods. (1) The theory of games with asymmetrical information shows that the right incentives allow hosts to screen-out parasites and screen-in mutualists, explaining successful partner choice in the absence of signalling. Applications range from ant-plants to microbiomes. (2) Contract theory distinguishes two longstanding but weakly differentiated explanations of host response to defectors: host sanctions and partner fidelity feedback. Host traits that selectively punish misbehaving symbionts are parsimoniously interpreted as pre-adaptations. Yucca-moth and legume-rhizobia mutualisms are argued to be examples of partner fidelity feedback. (3) The theory of public goods shows that cooperation in multi-player interactions can evolve in the absence of assortment, in one-shot social dilemmas among non-kin. Applications include alarm calls in vertebrates and exoenzymes in microbes. 2011 Blackwell Publishing Ltd/CNRS.
Network Security Validation Using Game Theory
Papadopoulou, Vicky; Gregoriades, Andreas
Non-functional requirements (NFR) such as network security recently gained widespread attention in distributed information systems. Despite their importance however, there is no systematic approach to validate these requirements given the complexity and uncertainty characterizing modern networks. Traditionally, network security requirements specification has been the results of a reactive process. This however, limited the immunity property of the distributed systems that depended on these networks. Security requirements specification need a proactive approach. Networks' infrastructure is constantly under attack by hackers and malicious software that aim to break into computers. To combat these threats, network designers need sophisticated security validation techniques that will guarantee the minimum level of security for their future networks. This paper presents a game-theoretic approach to security requirements validation. An introduction to game theory is presented along with an example that demonstrates the application of the approach.
Game Theory in water resources management
Katsanevaki, Styliani Maria; Varouchakis, Emmanouil; Karatzas, George
2015-04-01
Rural water management is a basic requirement for the development of the primary sector and involves the exploitation of surface/ground-water resources. Rational management requires the study of parameters that determine their exploitation mainly environmental, economic and social. These parameters reflect the influence of irrigation on the aquifer behaviour and on the level-streamflow of nearby rivers as well as on the profit from the farming activity for the farmers' welfare. The question of rural water management belongs to the socio-political problems, since the factors involved are closely related to user behaviour and state position. By applying Game Theory one seeks to simulate the behaviour of the system 'surface/ground-water resources to water-users' with a model based on a well-known game, "The Prisoner's Dilemma" for economic development of the farmers without overexploitation of the water resources. This is a game of two players that have been extensively studied in Game Theory, economy and politics because it can describe real-world cases. The present proposal aims to investigate the rural water management issue that is referred to two competitive small partnerships organised to manage their agricultural production and to achieve a better profit. For the farmers' activities water is required and ground-water is generally preferable because consists a more stable recourse than river-water which in most of the cases in Greece are of intermittent flow. If the two farmer groups cooperate and exploit the agreed water quantities they will gain equal profits and benefit from the sustainable availability of the water recourses (p). If both groups overexploitate the resource to maximize profit, then in the medium-term they will incur a loss (g), due to the water resources reduction and the increase of the pumping costs. If one overexploit the resource while the other use the necessary required, then the first will gain great benefit (P), and the second will
GAME THEORY: MINIMISING THE COST OF CAPITAL VS. MAXIMISING THE RETURN OF INVESTORS
Directory of Open Access Journals (Sweden)
Mihaela Brindusa Tudose
2014-12-01
Full Text Available The application of game theory to financial transactions focuses on two categories of stakeholders: users of financing (firms and providers of financing (investors. The core of game theory consists in the strategy that a partner is able to build starting from the possible decisions of the other partner (each party having opposing interests. In fact, we deal here with a cooperative game in which both opponents seek to maximise their own chances of winning. The article aims to highlight the manner in which mathematical game theory is transposed in the field of corporate finance by balancing the firm’s objectives (maximising market value by minimising the cost of raising capital and the investors’ objectives (maximising returns on investments. The intended novelty of this paper lies in developing a model for optimising a firm’s financial structure and assessing it in terms of investors’ interests.
Using the Item Response Theory (IRT) for Educational Evaluation through Games
Euzébio Batista, Marcelo Henrique; Victória Barbosa, Jorge Luis; da Rosa Tavares, João Elison; Hackenhaar, Jonathan Luis
2013-01-01
This article shows the application of Item Response Theory (IRT) for educational evaluation using games. The article proposes a computational model to create user profiles, called Psychometric Profile Generator (PPG). PPG uses the IRT mathematical model for exploring the levels of skills and behaviors in the form of items and/or stimuli. The model…
Bakker, M.; Heuvel-Panhuizen, M.H.A.M. van den; Robitzsch, A.
2016-01-01
This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative
Peixoto, Mauricio Matos; Rand, David A J; Dynamics, Games and Science I
2011-01-01
"Dynamics, Games and Science I and II" are a selection of surveys and research articles written by leading researchers in mathematics and its applications to the sciences. The majority of the contributions are on dynamical systems and game theory, focusing either on some of their most fundamental and theoretical developments or on their applications to modeling in biology, economics, engineering, finances and psychology. The aim of these books is to present cutting-edge research in these areas that can encourage graduate students and researchers in mathematics to develop them further
Theory and practice in mathematics teacher education
DEFF Research Database (Denmark)
Østergaard, Kaj
2016-01-01
to the ATD, it is illustrated with an example on addition of fractions how the notions of didactic transposition and praxeology can be used to analyse the theory-practice relation in this situation. Build on this analysis, the two models are combined into a more comprehensive model for describing......The challenge of establishing an interplay between theory and practice in mathematics teacher education is examined by the use of the anthropological theory of the didactic (ATD). The theory-practice problem is described both in an international and a Danish context. After a brief introduction...
Mathematical theory of compressible fluid flow
von Mises, Richard
2004-01-01
A pioneer in the fields of statistics and probability theory, Richard von Mises (1883-1953) made notable advances in boundary-layer-flow theory and airfoil design. This text on compressible flow, unfinished upon his sudden death, was subsequently completed in accordance with his plans, and von Mises' first three chapters were augmented with a survey of the theory of steady plane flow. Suitable as a text for advanced undergraduate and graduate students - as well as a reference for professionals - Mathematical Theory of Compressible Fluid Flow examines the fundamentals of high-speed flows, with
The Interval Market Model in Mathematical Finance : Game Theoretic Methods
Bernhard, P.; Engwerda, J.C.; Roorda, B.; Schumacher, J.M.; Kolokoltsov, V.; Saint-Pierre, P.; Aubin, J.P.
2013-01-01
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous
Constraint theory multidimensional mathematical model management
Friedman, George J
2017-01-01
Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...
New paradigms of Game Theory from globalization
Directory of Open Access Journals (Sweden)
Francisco Javier Esquivel
2015-06-01
Full Text Available Games Theory constitutes a model by means every player tries to predict what they will make the other players in reply to his own actions, and to optimize the result of the above mentioned actions in his benefit knowing that the others are thinking to about the same form. The development of the theory supposed a boom after the World War II, which happened of analyzing exclusively competitive behaviors to considering situations with competitive and cooperative characteristics. Nevertheless, the advance of the humanity and the disappearance of both geopolitical blocks have eliminated the balance of power and have produced the emergence of a world the most based on the exclusive conquest of the power. This has originated the model change and dilemmas, happening from the most cooperative models (Prisoner’s Dilemma or from the models of the Cold War (Dilemma of the Gallina up to reaching the dilemmas of the Leader or of the Hero. This change of paradigm owes to the extension of the globalization, which originates an immeasurable loss of economic, social, political power, of human rights, which they have affected negatively to the poor people. In this paper is studied the change of paradigm caused by the consequences of the globalization and the geopolitical transformations in a monopolar world, analyzing the consequences on the basis of the Theory of Games.
The stability concept of evolutionary game theory a dynamic approach
1992-01-01
These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Personally, evolutionary game theory has given me the opportunity to transfer my enthusiasm for abstract mathematics to more practical pursuits. I was fortunate to have entered this field in its infancy when many biologists recognized its potential but were not prepared to grant it general acceptance. This is no longer the case. ESS theory is now a rapidly expanding (in both applied and theoretical directions) force that no evolutionary biologist can afford to ignore. Perhaps, to continue the life-cycle metaphor, ESS theory is now in its late adolescence and displays much of the optimism and exuberance of this exciting age. There are dangers in writing a text about a theory at this stage of development. A comprehensive treatment would involve too many loose ends for the reader to appreciate the central message. On the other hand, the current central m...
Philosophy of mathematics set theory, measuring theories, and nominalism
Preyer, Gerhard
2008-01-01
One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the ""indispensability argument"" of W. v. O.
[The mathematical theory of acupoints].
Zhuo, Lian-Shi
2013-12-01
The ancient medical classics were retrieved to explore narrative on acupoints. And the relevant content of legal calendar in Shiji (Historical Records) and Hanshu (History of the Former Han Dynasty) were taken as a reference. The result showed that the total number of acu-points were based on the number of 365 days of a year. And the corrupts can be restored with the theory of numerology. The 59 heat point originated from the phase of moon, while the 57 water points originated from the number or year related with diasters. Although acupoints are considered to be related with numerology, the recognition of hot points and water points are held to be associated with experiential points in clinic.
Mathematical methods in the theory of queuing
Khinchin, A Y; Quenouille, M H
2013-01-01
Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. The three-part treatment begins with a study of the stream of incoming demands (or ""calls,"" in the author's terminology). Subsequent sections explore systems with losses and systems allowing delay. Prerequisites include a familiarity with the theory of probability and mathematical analysis. A. Y. Khinchin made significant contributions to probability theory, statistical physics, and several other fields. His elegant, groundbreaking work will prove of subs
An Evolutionary Game Theory Model of Spontaneous Brain Functioning.
Madeo, Dario; Talarico, Agostino; Pascual-Leone, Alvaro; Mocenni, Chiara; Santarnecchi, Emiliano
2017-11-22
Our brain is a complex system of interconnected regions spontaneously organized into distinct networks. The integration of information between and within these networks is a continuous process that can be observed even when the brain is at rest, i.e. not engaged in any particular task. Moreover, such spontaneous dynamics show predictive value over individual cognitive profile and constitute a potential marker in neurological and psychiatric conditions, making its understanding of fundamental importance in modern neuroscience. Here we present a theoretical and mathematical model based on an extension of evolutionary game theory on networks (EGN), able to capture brain's interregional dynamics by balancing emulative and non-emulative attitudes among brain regions. This results in the net behavior of nodes composing resting-state networks identified using functional magnetic resonance imaging (fMRI), determining their moment-to-moment level of activation and inhibition as expressed by positive and negative shifts in BOLD fMRI signal. By spontaneously generating low-frequency oscillatory behaviors, the EGN model is able to mimic functional connectivity dynamics, approximate fMRI time series on the basis of initial subset of available data, as well as simulate the impact of network lesions and provide evidence of compensation mechanisms across networks. Results suggest evolutionary game theory on networks as a new potential framework for the understanding of human brain network dynamics.
Game theory: applications for surgeons and the operating room environment.
McFadden, David W; Tsai, Mitchell; Kadry, Bassam; Souba, Wiley W
2012-11-01
Game theory is an economic system of strategic behavior, often referred to as the "theory of social situations." Very little has been written in the medical literature about game theory or its applications, yet the practice of surgery and the operating room environment clearly involves multiple social situations with both cooperative and non-cooperative behaviors. A comprehensive review was performed of the medical literature on game theory and its medical applications. Definitive resources on the subject were also examined and applied to surgery and the operating room whenever possible. Applications of game theory and its proposed dilemmas abound in the practicing surgeon's world, especially in the operating room environment. The surgeon with a basic understanding of game theory principles is better prepared for understanding and navigating the complex Operating Room system and optimizing cooperative behaviors for the benefit all stakeholders. Copyright © 2012 Mosby, Inc. All rights reserved.
Data fusion mathematics theory and practice
Raol, Jitendra R
2015-01-01
Fills the Existing Gap of Mathematics for Data FusionData fusion (DF) combines large amounts of information from a variety of sources and fuses this data algorithmically, logically and, if required intelligently, using artificial intelligence (AI). Also, known as sensor data fusion (SDF), the DF fusion system is an important component for use in various applications that include the monitoring of vehicles, aerospace systems, large-scale structures, and large industrial automation plants. Data Fusion Mathematics: Theory and Practice offers a comprehensive overview of data fusion, and provides a
Games as Actors - Interaction, Play, Design, and Actor Network Theory
DEFF Research Database (Denmark)
Jessen, Jari Due; Jessen, Carsten
2014-01-01
When interacting with computer games, users are forced to follow the rules of the game in return for the excitement, joy, fun, or other pursued experiences. In this paper, we investigate how games a chieve these experiences in the perspective of Actor Network Theory (ANT). Based on a qualitative......, and by doing so they create in humans what in modern play theory is known as a “state of play”...
Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping.
Zhu, Xuli; Jiang, Libo; Ye, Meixia; Sun, Lidan; Gragnoli, Claudia; Wu, Rongling
2016-05-01
Natural selection has shaped the evolution of organisms toward optimizing their structural and functional design. However, how this universal principle can enhance genotype-phenotype mapping of quantitative traits has remained unexplored. Here we show that the integration of this principle and functional mapping through evolutionary game theory gains new insight into the genetic architecture of complex traits. By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability. Functional mapping provides a procedure for estimating the genetic parameters that specify the dynamic relationship of competition and cooperation and predicting how genes mediate the evolution of this relationship during trait formation. Copyright © 2016 Elsevier Ltd. All rights reserved.
Just Society as a Fair Game: John Rawls and Game Theory in the 1950s.
Gališanka, Andrius
2017-01-01
I explore the influence of game theory on the political philosopher John Rawls as a way of analyzing the character of his democratic thought. Recent narratives bring Rawls closer to direct democracy as a result of game theory's influence. I argue that game theory prompted creative, organic developments in Rawls's political framework rather than shaping it. It prompted Rawls to emphasize autonomy and fairness, leading him to the analogy between a just society and a fair game. And it prompted thought experiments that analyzed our considered judgments. This was an idealized analysis unconnected to the vision of direct democracy.
A Theory of Developing Competence with Written Mathematical Symbols.
Hiebert, James
1988-01-01
Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)
Making Decisions about an Educational Game, Simulation or Workshop: A 'Game Theory' Perspective.
Cryer, Patricia
1988-01-01
Uses game theory to help practitioners make decisions about educational games, simulations, or workshops whose outcomes depend to some extent on chance. Highlights include principles for making decisions involving risk; elementary laws of probability; utility theory; and principles for making decisions involving uncertainty. (eight references)…
Linear programming mathematics, theory and algorithms
1996-01-01
Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
A Mathematical Theory of System Information Flow
2016-06-27
i.i.d. is usually quite involved. There are numerous experiments , often using photons, to test Bell’s Inequality recorded in the literature, but the...classical setting. Peter focused on non-locality as an alternative theory and experiments using the CHSH inequality , and devised a statistical procedure...761 (2014). 7. BIERHORST, P., A new loophole in recent Bell test experiments , arXiv:1311.4488, (2014). 8. BIERHORST, P., A Mathematical Foundation
Water Waves The Mathematical Theory with Applications
Stoker, J J
2011-01-01
Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.
Implementation of quantum game theory simulations using Python
Madrid S., A.
2013-05-01
This paper provides some examples about quantum games simulated in Python's programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner's dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.
Guide to mathematical concepts of quantum theory
International Nuclear Information System (INIS)
Heinosaari, T.; Ziman, M.
2008-01-01
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory (Authors)
Guide to mathematical concepts of quantum theory
International Nuclear Information System (INIS)
Heinosaari, T.; Ziman, M.
2008-01-01
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)
Application of Game Theory Approaches in Routing Protocols for Wireless Networks
Javidi, Mohammad M.; Aliahmadipour, Laya
2011-09-01
An important and essential issue for wireless networks is routing protocol design that is a major technical challenge due to the function of the network. Game theory is a powerful mathematical tool that analyzes the strategic interactions among multiple decision makers and the results of researches show that applied game theory in routing protocol lead to improvement the network performance through reduce overhead and motivates selfish nodes to collaborate in the network. This paper presents a review and comparison for typical representatives of routing protocols designed that applied game theory approaches for various wireless networks such as ad hoc networks, mobile ad hoc networks and sensor networks that all of them lead to improve the network performance.
Wei, Fang-Yi Flora; Hendrix, Katherine Grace
2009-01-01
This study investigated whether competitive and noncompetitive educational mathematics computer games influence four- to seven-year-old boys' and girls' recall of game-playing experience. A qualitative analysis was performed to investigate what preschool children may have learned through their selective recall of game-playing experience. A…
Buschang, Rebecca E.; Chung, Gregory K. W. K.; Kim, Jinok
2011-01-01
This study is an exploratory study of the relationship between collaboration and mathematics and game outcomes in a video game aimed at teaching concepts related to rational numbers. The sample included 243 middle school students who played the video game either with one partner or individually for 40 minutes. Results suggest that participants…
A Computer-Based Game That Promotes Mathematics Learning More than a Conventional Approach
McLaren, Bruce M.; Adams, Deanne M.; Mayer, Richard E.; Forlizzi, Jodi
2017-01-01
Excitement about learning from computer-based games has been papable in recent years and has led to the development of many educational games. However, there are relatively few sound empirical studies in the scientific literature that have shown the benefits of learning mathematics from games as opposed to more traditional approaches. The…
Plass, Jan L.; O'Keefe, Paul A.; Homer, Bruce D.; Case, Jennifer; Hayward, Elizabeth O.; Stein, Murphy; Perlin, Ken
2013-01-01
The present research examined how mode of play in an educational mathematics video game impacts learning, performance, and motivation. The game was designed for the practice and automation of arithmetic skills to increase fluency and was adapted to allow for individual, competitive, or collaborative game play. Participants (N = 58) from urban…
Li, Qing; Vandermeiden, Elise; Lemieux, Collette; Nathoo, Shahista
2016-01-01
This study explored secondary students' learning experiences in mathematics through digital game building. In this study, students were asked to become designers and builders in order to coauthor their own mathematics learning. Grounded in enactivism, this study examined the impact of game building on students' achievement. In addition, it…
Effect of Digital Game Based Learning on Ninth Grade Students' Mathematics Achievement
Swearingen, Dixie K.
2011-01-01
This experimental study examined the effect of an educational massive multiplayer online game (MMOG) on achievement on a standards-based mathematics exam. It also examined the interaction of student characteristics (gender and socioeconomic status) with digital game play on mathematics achievement. Two hundred eighty ninth grade students from a…
Evaluation of Mathematical Game Design Skills of Pre-Service Classroom Teachers
Pilten, Pusat; Pilten, Gülhiz; Divrik, Ramazan; Divrik, Fatma
2017-01-01
The purpose of the research is to evaluate the games prepared by pre-service classroom teachers within the scope of "Mathematics Teaching 1" and "Mathematics Teaching 2" courses, which are included in the undergraduate classroom teaching programs in Turkey, and to make predictions on the game design skills of pre-service…
Attacking cancer dormacy using game theory
Austin, Robert
Here is the problem: Cancer kills primarily by re-emergence from a period of dormancy after initial treatment. The presence of driver mutations and subsequent clonal expansion by Darwinian evolution does not explain dormancy and re-emergence of cancer from a community of cancer and host cells (including stromal and immune cells), nor does it explain our inability to predict the emergence of metastasis, by far the real killer in cancer. Dormancy appears to be a slow-driven, multi-cell interaction-dominated, threshold system with a poor prognosis once the cancer emerges from dormancy. The mission here is to try and model the phenomena of dormancy using game theory ideas, and in an in vitro complex ecology designed to emulate the true complexity of an in vivo tumor.
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Models in cooperative game theory crisp, fuzzy, and multi-choice games
Branzei, Rodica; Tijs, Stef
2005-01-01
This book investigates models in cooperative game theory in which the players have the possibility to cooperate partially. In a crisp game the agents are either fully involved or not involved at all in coperation with some other agents, while in a fuzzy game players are allowed to cooperate with infinite many different participation levels, varying from non-cooperation to full cooperation. A multi-choice game describes the intermediate case in which each player may have a fixed number of activity levels. Different set and one-point solution concepts for these games are presented. The propertie
Energy Technology Data Exchange (ETDEWEB)
Hanauske, Matthias
2011-02-14
The evolution of socio-economic systems depend on the interdependent decision processes of its underlying system components. The mathematical model to describe the strategic decision of players within a socio-economic game is ''game theory''. ''Quantum game theory'' is a mathematical and conceptual amplification of classical game theory. The space of all conceivable decision paths is extended from the purely rational, measurable space in the Hilbert-space of complex numbers - which is the mathematical space where quantum theory is formulated. By the concept of a potential entanglement of the imaginary quantum strategy parts, it is possible to include cooperate decision path, caused by cultural or moral standards. If this strategy entanglement is large enough, then additional Nash equilibria can occur, previously present dominant strategies could become nonexistent and new evolutionary stable strategies do appear for some game classes. Within this PhD thesis the main results of classical and quantum games are summarized and all of the possible game classes of evolutionary (2 player)-(2 strategy) games are extended to quantum games. It is shown that the quantum extension of classical games with an underlying dilemma-like structure give different results, if the strength of strategic entanglement is above a certain barrier. After the German summary and the introduction paper, five different applications of the theory are discussed within the thesis. (orig.)
Lectures on mathematical theory of extremum problems
1972-01-01
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it doe...
Hense, Jan; Mandl, Heinz
2012-01-01
This conceptual paper aims to clarify the theoretical underpinnings of game based learning (GBL) and learning with digital learning games (DLGs). To do so, it analyses learning of game related skills and contents, which occurs constantly during playing conventional entertainment games, from three perspectives: learning theory, emotion theory, and…
On economic applications of evolutionary game theory
Daniel Friedman
1998-01-01
Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.
Graph Theory to Pure Mathematics: Some Illustrative Examples
Indian Academy of Sciences (India)
Graph Theory to Pure Mathematics: Some. Illustrative Examples v Yegnanarayanan is a. Professor of Mathematics at MNM Jain Engineering. College, Chennai. His research interests include graph theory and its applications to both pure maths and theoretical computer science. Keywords. Graph theory, matching theory,.
Spatial interaction models facility location using game theory
D'Amato, Egidio; Pardalos, Panos
2017-01-01
Facility location theory develops the idea of locating one or more facilities by optimizing suitable criteria such as minimizing transportation cost, or capturing the largest market share. The contributions in this book focus an approach to facility location theory through game theoretical tools highlighting situations where a location decision is faced by several decision makers and leading to a game theoretical framework in non-cooperative and cooperative methods. Models and methods regarding the facility location via game theory are explored and applications are illustrated through economics, engineering, and physics. Mathematicians, engineers, economists and computer scientists working in theory, applications and computational aspects of facility location problems using game theory will find this book useful.
Teaching Public Goods Theory with a Classroom Game
Pickhardt, Michael
2005-01-01
The author extends the work of Holt and Laury (1997) on a simple noncomputerized card game for teaching the essential aspects of public goods theory. He suggests a course of several lectures and discusses the behavior of subjects in various game sessions. Among other things, the results provide experimental evidence with respect to the private…
Game Theory and Educational Policy: Private Education Legislation in China
Law, Wing-Wah; Pan, Su-Yan
2009-01-01
This article presents a game theory analysis of legislating private education in China, based on set of primary and secondary documents related to this issue. The article argues that shaping educational legislation is a dynamic, repeated game of negotiation, cooperation, and/or competition on multiple occasions among various interested actors,…
On the Relevance of Game Theory in Strategic Thinking
African Journals Online (AJOL)
be used to predict the outcome of a strategy, explain why a particular outcome to a strategy ... concludes that game theory can aid decision makers at all levels in formulating quality strategies. In fact .... Also, for our argument, we assume that the USA has a free enterprise .... pay-offs based on the 2x2 game we find that.
Students Build Mathematical Theory: Semantic Warrants in Argumentation
Walter, Janet G.; Barros, Tara
2011-01-01
In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…
Mahmoudinia, D.; Esfahani, Rahim Dalali; Engwerda, Jacob; Dastjerdi, R.B.
2016-01-01
In this study, we follow several purpose. In the first section, the game theory concept and the formation of its fundamental concepts is examined. After that, we investigate that how von Neumann-Morgenstern (1944) and john Nash (1950-1953) works, caused the formation of modern game theory. Then, we
Mirawati
2017-02-01
The research departed from an issue found regarding the number sense of kindergarten children and as a solution to this problem, the research proposes the use of creative mathematical games in the teaching and learning. Departing from the issue and the offered solution, the following problems are about Children’s ability of number sense before and after the implementation of creative mathematical games; the forms of creative mathematical games in improving children’s number sense; the implementation of creative mathematical games in improving children’s number sense; and the factors possibly affecting the implementation of creative mathematical games. This study use action research method. The data were collected through observation, interview, and documentation and then qualitatively analysed using thematic analysis technique. The findings show that children respond positively to the creative mathematical games. They demonstrate fairly high enthusiasm and are able to understand number as well as its meaning in various ways. Children’s number sense has also improved in terms of one-on-one correspondence and mentioning and comparing many objects. The factors possibly affecting the implementation of these creative mathematical games are the media and the stages of teaching and learning that should be in accordance with the level of kindergarten children’s number sense.
The Use of Game Theory for Making Rational Decisions in Business Negations: A Conceptual Model
Directory of Open Access Journals (Sweden)
Kestutis Peleckis
2016-02-01
Full Text Available Objective: The objective of this paper is a comparative analysis of the world literature on game theory and its applicability for rational decision-making in negotiations and creation of a model supporting strategic decisions in negotiations. Research Design & Methods: Systematic, comparative, logical analysis and synthesis of the scientific literature. In order to create an algorithm of negotiations statements on theory of graphs, game theory and theory of heuristic algorithm were applied. Findings: The article proposes an algorithm which combines the game theory approach with heuristic algorithms in order to reflect the specifics of negotiations better. Such an algorithm can be used to support strategic decisions in negotiations and is useful for better understanding of the strategic management of negotiating processes. Implications & Recommendations: The proposed mathematical algorithm for the strategy formulation of international business negotiations can be used in electronic business negotiations, both as a standalone tool, or as partially requiring support by the negotiator. Contribution & Value Added: The game theory methods support rational solutions in business negotiations, as they enable to analyse the interacting forces. This is particularly relevant in international business negotiations, where participants from different cultures can be faced with numerous uncertainties.
The Correlation between Game Theory and International Trade
Directory of Open Access Journals (Sweden)
Simona-Valeria TOMA
2012-08-01
Full Text Available The Correlation between Game Theory and International TradeAbstract:Game theory, in its most basic form, considers two or more players and analyses the different strategies that they can use and the effect that these strategies will have on each player. International trade allows countries to use better their resources (labor, technology or capital. Since countries have different capital or natural resources, some of them will produce a good more efficiently than others and therefore could sell it cheaper than other countries. By using game theory in international trade we could determine if the Heckscher-Ohlin-Samuelson model is correct and what would be the best specialization for each country. The aim of this paper is to test if game theory could be successfully used in a thorough analysis of international trade specialization.
The cooperative game theory of networks and hierarchies
Gilles, Robert P
2010-01-01
This book details standard concepts in cooperative game theory with applications to the analysis of social networks and hierarchical authority organizations. It covers the multi-linear extension, the Core, the Shapley value, and the cooperative potential.
Video Game Characters. Theory and Analysis
Felix Schröter; Jan-Noël Thon
2014-01-01
This essay develops a method for the analysis of video game characters based on a theoretical understanding of their medium-specific representation and the mental processes involved in their intersubjective construction by video game players. We propose to distinguish, first, between narration, simulation, and communication as three modes of representation particularly salient for contemporary video games and the characters they represent, second, between narrative, ludic, and social experien...
Introduction to the theory of cooperative games
Peleg, Bezalel; Peleg, Bezalel
2007-01-01
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.
Panagiotakopoulos, Chris T.
2011-01-01
Mathematics is an area of study that particularly lacks student enthusiasm. Nevertheless, with the help of educational games, any phobias concerning mathematics can be considerably decreased and mathematics can become more appealing. In this study, an educational game addressing mathematics was designed, developed and evaluated by a sample of 33…
Video Game Characters. Theory and Analysis
Directory of Open Access Journals (Sweden)
Felix Schröter
2014-06-01
Full Text Available This essay develops a method for the analysis of video game characters based on a theoretical understanding of their medium-specific representation and the mental processes involved in their intersubjective construction by video game players. We propose to distinguish, first, between narration, simulation, and communication as three modes of representation particularly salient for contemporary video games and the characters they represent, second, between narrative, ludic, and social experience as three ways in which players perceive video game characters and their representations, and, third, between three dimensions of video game characters as ‘intersubjective constructs’, which usually are to be analyzed not only as fictional beings with certain diegetic properties but also as game pieces with certain ludic properties and, in those cases in which they function as avatars in the social space of a multiplayer game, as representations of other players. Having established these basic distinctions, we proceed to analyze their realization and interrelation by reference to the character of Martin Walker from the third-person shooter Spec Ops: The Line (Yager Development 2012, the highly customizable player-controlled characters from the role-playing game The Elder Scrolls V: Skyrim (Bethesda 2011, and the complex multidimensional characters in the massively multiplayer online role-playing game Star Wars: The Old Republic (BioWare 2011-2014.
Mathematical theory of elasticity of quasicrystals and its applications
Fan, Tianyou
2011-01-01
This book presents a clear-cut, strict and systematic mathematical overview of the continuum mechanics of novel materials, condensed matter physics and partial differential equations, and explores the mathematical theory of elasticity of quasicrystals.
Group Decisions in Biodiversity Conservation: Implications from Game Theory
Frank, David M.; Sarkar, Sahotra
2010-01-01
Background Decision analysis and game theory [1], [2] have proved useful tools in various biodiversity conservation planning and modeling contexts [3]?[5]. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto?inefficient Nash equilibria. These are cases in which each agent pursuing individual self?interest leads to a worse outcome for all, relative to other feasible outcomes....
Mathematical problems in wave propagation theory
1970-01-01
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surf...
Directory of Open Access Journals (Sweden)
P. Chitra
2017-04-01
Full Text Available Recently, wireless network technologies were designed for most of the applications. Congestion raised in the wireless network degrades the performance and reduces the throughput. Congestion-free network is quit essen- tial in the transport layer to prevent performance degradation in a wireless network. Game theory is a branch of applied mathematics and applied sciences that used in wireless network, political science, biology, computer science, philosophy and economics. e great challenges of wireless network are their congestion by various factors. E ective congestion-free alternate path routing is pretty essential to increase network performance. Stackelberg game theory model is currently employed as an e ective tool to design and formulate conges- tion issues in wireless networks. is work uses a Stackelberg game to design alternate path model to avoid congestion. In this game, leaders and followers are selected to select an alternate routing path. e correlated equilibrium is used in Stackelberg game for making better decision between non-cooperation and cooperation. Congestion was continuously monitored to increase the throughput in the network. Simulation results show that the proposed scheme could extensively improve the network performance by reducing congestion with the help of Stackelberg game and thereby enhance throughput.
Examining Student-Designed Games through Suits' Theory of Games
Casey, Ashley; Hastie, Peter; Jump, Steve
2016-01-01
This paper documents how a unit of student-designed games can create a more meaningful version of physical education (PE) for disengaged students, a version that enhances the educational legitimacy of the subject matter by affording it worth in and of itself rather than being justified for other, extrinsic or instrumental reasons. Furthermore, it…
Quantum game theory based on the Schmidt decomposition
International Nuclear Information System (INIS)
Ichikawa, Tsubasa; Tsutsui, Izumi; Cheon, Taksu
2008-01-01
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric games and obtain a complete set of quantum Nash equilibria. Apart from those available with the maximal entanglement, these quantum Nash equilibria are extensions of the Nash equilibria in classical game theory. The phase structure of the equilibria is determined for all values of entanglement, and thereby the possibility of resolving the dilemmas by entanglement in the game of Chicken, the Battle of the Sexes, the Prisoners' Dilemma, and the Stag Hunt, is examined. We find that entanglement transforms these dilemmas with each other but cannot resolve them, except in the Stag Hunt game where the dilemma can be alleviated to a certain degree
Conlin, Peter L; Chandler, Josephine R; Kerr, Benjamin
2014-10-01
In this review, we demonstrate how game theory can be a useful first step in modeling and understanding interactions among bacteria that produce and resist antibiotics. We introduce the basic features of evolutionary game theory and explore model microbial systems that correspond to some classical games. Each game discussed defines a different category of social interaction with different resulting population dynamics (exclusion, coexistence, bistability, cycling). We then explore how the framework can be extended to incorporate some of the complexity of natural microbial communities. Overall, the game theoretical perspective helps to guide our expectations about the evolution of some forms of antibiotic resistance and production because it makes clear the precise nature of social interaction in this context. Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Swami Iyer
Full Text Available The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.
Iyer, Swami; Reyes, Joshua; Killingback, Timothy
2014-01-01
The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.
Iyer, Swami; Reyes, Joshua; Killingback, Timothy
2014-01-01
The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games. PMID:24709851
Game Theory - Its Applications to Ethical Decision Making
Directory of Open Access Journals (Sweden)
Cavagnetto Stefano
2014-01-01
Full Text Available The application of game theory according to Hargreaves-Heap and Varonfakis (1995 to understand human behaviour, and in particular ethical behaviour, is a valuable development, as game theory has gradually become one of the key frameworks to assist us in the understanding of social sciences. Esther (1982 and Aumann and Hart (1992 show that there are several studies that indicate the importance of a game theoretic framework in advancing our understanding of social behaviour and evolutionary sciences. Although the application of game theory in the above areas has largely been not formalised, its application in the fields of ethical conduct and human behaviour is at present developed in several respects with the gradual assistance of advances in related areas such as evolutionary biology and our understanding of group social behaviour.
Experimental game theory and behavior genetics.
Cesarini, David; Dawes, Christopher T; Johannesson, Magnus; Lichtenstein, Paul; Wallace, Björn
2009-06-01
We summarize the findings from a research program studying the heritability of behavior in a number of widely used economic games, including trust, dictator, and ultimatum games. Results from the standard behavior genetic variance decomposition suggest that strategies and fundamental economic preference parameters are moderately heritable, with estimates ranging from 18 to 42%. In addition, we also report new evidence on so-called "hyperfair" preferences in the ultimatum game. We discuss the implications of our findings with special reference to current efforts that seek to understand the molecular genetic architecture of complex social behaviors.
Moral calculations game theory, logic, and human frailty
Mérő, László
1998-01-01
Are people ever rational? Consider this: You auction off a one-dollar bill to the highest bidder, but you set the rules so that the second highest bidder also has to pay the amount of his last bid, even though he gets nothing. Would people ever enter such an auction? Not only do they, but according to Martin Shubik, the game's inventor, the average winning bid (for a dollar, remember) is $3.40. Many winners report that they bid so high only because their opponent "went completely crazy." This game lies at the intersection of three subjects of eternal fascination: human psychology, morality, and John von Neumann's game theory. Hungarian game-theorist Laszlo Mero introduces us to the basics of game theory, including such concepts as zero-sum games, Prisoner's Dilemma and the origins of altruism; shows how game theory is applicable to fields ranging from physics to politics; and explores the role of rational thinking in the context of many different kinds of thinking. This fascinating, urbane book will interest ...
Using video games to combine learning and assessment in mathematics education
Kristian Juha Mikael Kiili; Keith Devlin; Arttu Perttula; Pauliina Tuomi; Antero Lindstedt
2015-01-01
One problem with most education systems is that learning and (summative) assessment are generally treated as quite separate things in schools. We argue that video games can provide an opportunity to combine these processes in an engaging and effective way. The present study focuses on investigating the effectiveness and the assessment power of two different mathematics video games, Semideus and Wuzzit Trouble. In the current study, we validated the Semideus game as a rational number test inst...
Bakker, Marjoke; van den Heuvel-Panhuizen, Marja; Robitzsch, Alexander
2016-01-01
This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons…
Bakker, M.|info:eu-repo/dai/nl/355337770; Van den Heuvel-Panhuizen, M.|info:eu-repo/dai/nl/069266255; Robitzsch, Alexander
2016-01-01
This study examined the effects of a teacher-delivered intervention with online math-ematics mini-games on special education students’ multiplicative reasoning ability(multiplication and division). The games involved declarative, procedural, as well asconceptual knowledge of multiplicative
The mathematics of games an introduction to probability
Taylor, David G
2014-01-01
Dice, Coins, and Candy Introduction ProbabilityCandy (Yum)! Wheels and More Dice RouletteCrapsCounting the Pokers Cards and CountingSeven Card Pokers Texas Hold'Em BluffingWindmills and Black Jacks? Blackjack Blackjack VariantsMore Fun Dice!Liar's Dice Yahtzee Zombie Dice Board Games, Not ""Bored"" Games Board Game Movement Pay Day (The Board Game) MonopolySpread, RevisitedCan You Bet and Win? Betting SystemsGambler's RuinThere Are More Games! The LotteryBingo Baccarat Farkle BackgammonMemoryAppendices A Probabilities with Infinity B St. Petersburg Paradox C Prisoner's Dilemma and More Game Th
Game theory and extremal optimization for community detection in complex dynamic networks.
Lung, Rodica Ioana; Chira, Camelia; Andreica, Anca
2014-01-01
The detection of evolving communities in dynamic complex networks is a challenging problem that recently received attention from the research community. Dynamics clearly add another complexity dimension to the difficult task of community detection. Methods should be able to detect changes in the network structure and produce a set of community structures corresponding to different timestamps and reflecting the evolution in time of network data. We propose a novel approach based on game theory elements and extremal optimization to address dynamic communities detection. Thus, the problem is formulated as a mathematical game in which nodes take the role of players that seek to choose a community that maximizes their profit viewed as a fitness function. Numerical results obtained for both synthetic and real-world networks illustrate the competitive performance of this game theoretical approach.
Modeling Routinization in Games: An Information Theory Approach
DEFF Research Database (Denmark)
Wallner, Simon; Pichlmair, Martin; Hecher, Michael
2015-01-01
Routinization is the result of practicing until an action stops being a goal-directed process. This paper formulates a definition of routinization in games based on prior research in the fields of activity theory and practice theory. Routinization is analyzed using the formal model of discrete......-time, discrete-space Markov chains and information theory to measure the actual error between the dynamically trained models and the player interaction. Preliminary research supports the hypothesis that Markov chains can be effectively used to model routinization in games. A full study design is presented...
Directory of Open Access Journals (Sweden)
Hasan Topçu
2014-08-01
Full Text Available The aim of this study was to reveal the opinions of elementary school pre-service teachers about the usage of educational mathematics games in elementary mathematics teaching. In this study, case study that, one of qualitative research methods, was used. Data were collected by utilizing a semi-structured interview form to these elementary school pre-service teachers and analyzed using by content analysis method. A total of 10 junior pre-service teachers enrolled in undergraduate programs of elementary teaching attended to this research. In conclusion, these pre-service teachers indicated that educational computer games would provide benefits such as making students’ learning more permanent, visualizing concepts, making students love mathematics, learning by entertaining, reinforcing what has been learnt and developing thinking skills. Nevertheless, these elementary school pre-service teachers stated the limitations about educational computer games such as causing addiction and physical damages, being time-consuming, requiring special equipment and software and making class management difficult. Besides, it was revealed that the pre-service teachers demonstrated positive attitudes towards the use of games in courses while that they did not feel themselves competent in terms of application.Key Words: Educational computer games, mathematics teaching, elementary school pre-service teachers
Integrating Health Behavior Theory and Design Elements in Serious Games.
Cheek, Colleen; Fleming, Theresa; Lucassen, Mathijs Fg; Bridgman, Heather; Stasiak, Karolina; Shepherd, Matthew; Orpin, Peter
2015-01-01
Internet interventions for improving health and well-being have the potential to reach many people and fill gaps in service provision. Serious gaming interfaces provide opportunities to optimize user adherence and impact. Health interventions based in theory and evidence and tailored to psychological constructs have been found to be more effective to promote behavior change. Defining the design elements which engage users and help them to meet their goals can contribute to better informed serious games. To elucidate design elements important in SPARX, a serious game for adolescents with depression, from a user-centered perspective. We proposed a model based on an established theory of health behavior change and practical features of serious game design to organize ideas and rationale. We analyzed data from 5 studies comprising a total of 22 focus groups and 66 semistructured interviews conducted with youth and families in New Zealand and Australia who had viewed or used SPARX. User perceptions of the game were applied to this framework. A coherent framework was established using the three constructs of self-determination theory (SDT), autonomy, competence, and relatedness, to organize user perceptions and design elements within four areas important in design: computer game, accessibility, working alliance, and learning in immersion. User perceptions mapped well to the framework, which may assist developers in understanding the context of user needs. By mapping these elements against the constructs of SDT, we were able to propose a sound theoretical base for the model. This study's method allowed for the articulation of design elements in a serious game from a user-centered perspective within a coherent overarching framework. The framework can be used to deliberately incorporate serious game design elements that support a user's sense of autonomy, competence, and relatedness, key constructs which have been found to mediate motivation at all stages of the change
Mathematical and physical aspects of gauge theories
International Nuclear Information System (INIS)
Chatelet, G.; Paris-13 Univ., 93 - Saint-Denis
1981-01-01
We present here a survey of gauge theories, trying to relate the main mathematical and physical concepts. Part I is devoted to exhibiting parallel transport and connection as the adequate concepts for the constitution of the parametrized internal space of a particle. A covariant derivative provides the differential calculus, which is needed when one leaves the point-like description in microphysics. Part II deals with the so-called pure gauge theory and sketches the construction of the self-dual solutions of Yang-Mills equations. We briefly explain Guersey's method to get SU 2 self-dual potentials as quarternionic analytic maps from S 4 (first quarternionic projective space) into HPsub(n) (n-dimensional quarternionic projective space). Part III is devoted to the Goldstone's theorem and Higgs' mechanism used to provide a mass to gauge mesons. We describe a Salam-Weinberg model to illustrate these techniques. Part IV deals with the perturbative aspect. The Faddeev-Popov method, formerly conceived as a technique to get correct Feynmann rules, actually leads to a systematic study of the affine space of connections factored out by gauge transformations. (orig.)
Route Choice Model Based on Game Theory for Commuters
Directory of Open Access Journals (Sweden)
Licai Yang
2016-06-01
Full Text Available The traffic behaviours of commuters may cause traffic congestion during peak hours. Advanced Traffic Information System can provide dynamic information to travellers. Due to the lack of timeliness and comprehensiveness, the provided information cannot satisfy the travellers’ needs. Since the assumptions of traditional route choice model based on Expected Utility Theory conflict with the actual situation, a route choice model based on Game Theory is proposed to provide reliable route choice to commuters in actual situation in this paper. The proposed model treats the alternative routes as game players and utilizes the precision of predicted information and familiarity of traffic condition to build a game. The optimal route can be generated considering Nash Equilibrium by solving the route choice game. Simulations and experimental analysis show that the proposed model can describe the commuters’ routine route choice decisionexactly and the provided route is reliable.
"Depletion": A Game with Natural Rules for Teaching Reaction Rate Theory.
Olbris, Donald J.; Herzfeld, Judith
2002-01-01
Depletion is a game that reinforces central concepts of reaction rate theory through simulation. Presents the game with a set of follow-up questions suitable for either a quiz or discussion. Also describes student reaction to the game. (MM)
Enhancing Undergraduate Mathematics Curriculum via Coding Theory and Cryptography
Aydin, Nuh
2009-01-01
The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…
Cognitive Hierarchy Theory and Two-Person Games
Directory of Open Access Journals (Sweden)
Carlos Gracia-Lázaro
2017-01-01
Full Text Available The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i any snowdrift game can be characterized by only a parameter, its class; (ii they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory.
The Effect of Teams Games Tournament on Mathematics Self-Efficacy in Junior High Schools
Directory of Open Access Journals (Sweden)
Annurwanda Pradipta
2018-01-01
Full Text Available Teams Games Tournament is one cooperative learning method which actively involves students to solve their problems through an interesting game. The game consists of questions that have content relevant to the main topic and to boost up students’ self-confidence in their ability to exert their self-control over motivation, behavior and social environment. This research aims at investigating the effect of Teams Games Tournament toward students’ self-efficacy on mathematics. The study was conducted toward 64 seventh graders in Landak Regency on social arithmetic material, selected using cluster random sampling. The experimental design used the one group pretest posttest experimental design that was analyzed by quantitative method. Data collection employed "Mathematics Self Efficacy Questionnaire" and was analyzed by statistical method using SPSS-20. The results show that Teams Games Tournament has a significant effect toward students’ self-efficacy on mathematics. The result is drawn from t-value = -12.369 and sig.(2-tailed = 0.00. Therefore, it can be concluded that Teams Games Tournament has positive effect toward students’ self-efficacy on mathematics. The study implies that teachers should consider the implementation of Teams Games Tournament in classroom teaching.
Using video games to combine learning and assessment in mathematics education
Directory of Open Access Journals (Sweden)
Kristian Juha Mikael Kiili
2015-12-01
Full Text Available One problem with most education systems is that learning and (summative assessment are generally treated as quite separate things in schools. We argue that video games can provide an opportunity to combine these processes in an engaging and effective way. The present study focuses on investigating the effectiveness and the assessment power of two different mathematics video games, Semideus and Wuzzit Trouble. In the current study, we validated the Semideus game as a rational number test instrument. We used it as a pre- and a post-test for a three-hour intervention in which we studied the effectiveness of Wuzzit Trouble, a game built on whole number arithmetic and designed to enhance mathematical thinking and problem solving skills. The results showed that (1 games can be used to assess mathematical knowledge validly, and (2 even short game-based interventions can be very effective. Based on the results, we argue that game-based assessment can create a more complete picture of mathematical knowledge than simply measuring students' accuracy, providing indicators of student misconceptions and conceptual change processes
Computer Game Theories for Designing Motivating Educational Software: A Survey Study
Ang, Chee Siang; Rao, G. S. V. Radha Krishna
2008-01-01
The purpose of this study is to evaluate computer game theories for educational software. We propose a framework for designing engaging educational games based on contemporary game studies which includes ludology and narratology. Ludology focuses on the study of computer games as play and game activities, while narratology revolves around the…
Directory of Open Access Journals (Sweden)
Claus Toft-Nielsen
2015-05-01
Full Text Available This article investigates digital game play (gaming as a specific media field (Bourdieu, 1984, p. 72, in which especially gaming capital (Consalvo, 2007 functions as a theoretical lens. We aim to analyse the specific practices that constitute and are constituted in and around gaming. This multitude of practices is theoretically qualified by the second generation of practice theorists, including (Bruchler & Postill, 2010; Reckwitz, 2002; Schatzki, 2008; Warde, 2005. The empirical data are drawn from qualitative studies of gamers and gaming practices (focus groups as well as participant observations, and function as exemplary cases that illustrate our theoretical arguments. Our purpose is to analytically operationalize field theory, by means of practice theory, to enhance our understanding of digital games as new media and the specific contexts and media practices herein.
DEFF Research Database (Denmark)
Toft-Nielsen, Claus; Krogager, Stinne Gunder Strøm
2015-01-01
This article investigates digital game play (gaming) as a specific media field (Bourdieu, 1984, p. 72), in which especially gaming capital (Consalvo, 2007) functions as a theoretical lens. We aim to analyse the specific practices that constitute and are constituted in and around gaming....... This multitude of practices is theoretically qualified by the second generation of practice theorists, including (Bruchler & Postill, 2010; Reckwitz, 2002; Schatzki, 2008; Warde, 2005). The empirical data are drawn from qualitative studies of gamers and gaming practices (focus groups as well as participant...... observations), and function as exemplary cases that illustrate our theoretical arguments. Our purpose is to analytically operationalize field theory, by means of practice theory, to enhance our understanding of digital games as new media and the specific contexts and media practices herein....
Positioning in Mathematics Education: Revelations on an Imported Theory
Herbel-Eisenmann, Beth A.; Wagner, David; Johnson, Kate R.; Suh, Heejoo; Figueras, Hanna
2015-01-01
We develop theory within the field of mathematics education based on analysis of an imported theory--positioning theory--and the way it is used in the field. After summarizing positioning theory, we identify some conceptual fuzziness, particularly in core terms "positioning" and "storyline." We offer Lemke's idea of timescales…
Veloo, Arsaythamby; Md-Ali, Ruzlan; Chairany, Sitie
2016-01-01
Purpose: This paper was part of a larger study which looked into the effect of implementing Cooperative Teams-Games-Tournament (TGT) on understanding of and communication in mathematics. The study had identified the main and interaction effect of using Cooperative TGT for learning mathematics in religious secondary school classrooms. A…
Bragg, Leicha
2007-01-01
Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator…
Students' Perceptions of the Learning Environment and Attitudes in Game-Based Mathematics Classrooms
Afari, Ernest; Aldridge, Jill M.; Fraser, Barry J.; Khine, Myint Swe
2013-01-01
We investigated whether the introduction of games into college-level mathematics classes in the United Arab Emirates (UAE) was effective in terms of improving students' perceptions of the learning environment and their attitudes towards of mathematics. A pre-post design involved the administration of English and Arabic versions of two surveys (one…
Digital Educational Games and Mathematics. Results of a Case Study in Primary School Settings
Fokides, Emmanuel
2018-01-01
The study presents the results of a project in which a series of digital games were used for teaching Mathematics to first, fourth, and sixth-grade primary school students (ages 6-7, 8-9, and 11-12). Mathematics was selected as the teaching subject because of the difficulties students face in understanding basic math concepts. Although digital…
Game theory as a conceptual framework for managing insect pests.
Brown, Joel S; Staňková, Kateřina
2017-06-01
For over 100 years it has been recognized that insect pests evolve resistance to chemical pesticides. More recently, managers have advocated restrained use of pesticides, crop rotation, the use of multiple pesticides, and pesticide-free sanctuaries as resistance management practices. Game theory provides a conceptual framework for combining the resistance strategies of the insects and the control strategies of the pest manager into a unified conceptual and modelling framework. Game theory can contrast an ecologically enlightened application of pesticides with an evolutionarily enlightened one. In the former case the manager only considers ecological consequences whereas the latter anticipates the evolutionary response of the pests. Broader applications of this game theory approach include anti-biotic resistance, fisheries management and therapy resistance in cancer. Copyright © 2017 Elsevier Inc. All rights reserved.
Academic Training Lecture | Game Theory | 8 - 9 May
2014-01-01
Game Theory (1 & 2), by Elias Koutsoupias (Professor of Computer Science, University of Oxford, UK). Thursday 8 May and Friday 9 May from 11 a.m. to 12 a.m. CERN (500-1-001 - Main Auditorium) Description: This lecture series will present the main directions of Algorithmic Game Theory, a new field that has emerged in the last two decades at the interface of Game Theory and Computer Science, because of the unprecedented growth in size, complexity, and impact of the Internet and the Web. These include the price of anarchy (what is the impact of selfishness on a system of competing entities), computational complexity (can the market find a reasonable solution), mechanisms and auctions (what incentives to give to selfish individuals). See the Indico page here.
Signal to act : game theory in pragmatics
Franke, M.
2009-01-01
This thesis offers a general game theoretic model of language use and interpretation and applies it to linguistic pragmatics in the vein of Grice (1989). The model presented here —called the ibr model explains pragmatic phenomena, such as conversational implicatures, as arising from a sequence of
Mathematical theories of classical particle channeling in perfect crystals
International Nuclear Information System (INIS)
Dumas, H. Scott
2005-01-01
We present an overview of our work on rigorous mathematical theories of channeling for highly energetic positive particles moving in classical perfect crystal potentials. Developed over the last two decades, these theories include: (i) a comprehensive, highly mathematical theory based on Nekhoroshev's theorem which embraces both axial and planar channeling as well as certain non-channeling particle motions (ii) a theory of axial channeling for relativistic particles based on a single-phase averaging method for ordinary differential equations and (iii) a theory of planar channeling for relativistic particles based on a two-phase averaging method for ordinary differential equations. Here we touch briefly on (i) and (ii), then focus on (iii). Together these theories place Lindhard's continuum model approximations on a firm mathematical foundation, and should serve as the starting point for more refined mathematical treatments of channeling
Quantum information theory. Mathematical foundation. 2. ed.
International Nuclear Information System (INIS)
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics - all of which are addressed here - made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
Quantum information theory. Mathematical foundation. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Masahito [Nagoya Univ. (Japan). Graduate School of Mathematics
2017-07-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics - all of which are addressed here - made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
A Game Theory Approach for Product Specialization in International Trade
Directory of Open Access Journals (Sweden)
Ioana-Veronica ALEXA
2011-11-01
Full Text Available Game theory, in its most basic form, considers two players and analyses the different strategies that they can use and the effect that these strategies will have on each player. International trade allows countries to use better their resources (labor, technology or capital. Since countries have different capital or natural resources, some of them will produce a good more efficiently than others and therefore could sell it cheaper than other countries. By using game theory in international trade we could determine if the H-O-S model is correct and what would be the best specialization for each country.
Index Theory with Applications to Mathematics and Physics
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, David
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has giv...... birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence.......Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given...
Topics in the mathematical physics of E-infinity theory
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
This is the fourth contribution in a series of papers aimed at directing the attention of the prospective E-infinity researcher to the most important mathematical background and sources needed for an easy understanding and successful application of this theory. The present paper is mainly concerned with the mathematical physics relevant to E-infinity theory with emphasis on super Yang-Mills theory and superstrings
Intelligent mathematics II applied mathematics and approximation theory
Duman, Oktay
2016-01-01
This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.
The Application of Gaming Theory in Health Care.
Elzein, Ashley; Drenkard, Karen; Deyo, Patricia; Swartwout, Ellen
2015-01-01
As the US health care system moves rapidly toward a population health management focus in communities and care settings, the chief nursing officer has an opportunity to lead innovation efforts for patient care. One innovative strategy for use to influence patient behavior change, ongoing clinical education, and prelicensure education is the application of gaming theory into learning strategies. With the ever-increasing emphasis the general public is placing on social media and online gaming, there has been a significant push by the health sector in recent years to harness this medium for use in health management, education, and behavior change. A number of organizations and insurers have dedicated significant resources to researching and developing games and apps to help patients manage diseases, track self-management activities, and motivate behavior change for healthy lifestyles. This article shares information about gaming theory and its application to health care including a review of the science behind the theory, the use of technology, and gaming education strategies for both patients and clinicians.
Towards a simple mathematical theory of citation distributions.
Katchanov, Yurij L
2015-01-01
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.
The Effect of using Teams Games Tournaments (TGT Technique for Learning Mathematics in Bangladesh
Directory of Open Access Journals (Sweden)
Abdus Salam
2015-07-01
Full Text Available Games-based learning has captured the interest of educationalists and industrialists who seek to reveal the characteristics of computer games as they are perceived by some to be a potentially effective approach for teaching and learning. Despite this interest in using games-based learning, there is a dearth of studies context of gaming and education in third world countries. This study investigated the effects of game playing on performance and attitudes of students towards mathematics of Grade VIII. The study was undergone by implementing TGT technique for the experimental group and typical lecture-based approach for the control group. A same achievement test was employed as in both pretest and post test, an inventory of attitudes towards mathematics were applied for the pretest and post test on TGT experimental and control group, an attitude scale on computer games was employed for the TGT experimental group, a semi-structured interview for teacher and an FGD guideline for students were applied to serving the purpose of research objectives. After three-weeks of intervention, it had been found out that TGT experimental group students had achieved a significant learning outcome than lecture based control group students. Attitude towards mathematics were differed to a certain positive extent on TGT experimental group. On the basis of findings of this study, some recommendations were made to overcome the barriers of integrating web-based game playing in a classroom.
Hefetz, Dan; Stojaković, Miloš; Szabó, Tibor
2014-01-01
This text serves as a thorough introduction to the rapidly developing field of positional games. This area constitutes an important branch of combinatorics, whose aim it is to systematically develop an extensive mathematical basis for a variety of two-player perfect information games. These range from such popular games as Tic-Tac-Toe and Hex to purely abstract games played on graphs and hypergraphs. The subject of positional games is strongly related to several other branches of combinatorics such as Ramsey theory, extremal graph and set theory, and the probabilistic method. These notes cover a variety of topics in positional games, including both classical results and recent important developments. They are presented in an accessible way and are accompanied by exercises of varying difficulty, helping the reader to better understand the theory. The text will benefit both researchers and graduate students in combinatorics and adjacent fields.
Review of game theory applications for situation awareness
Blasch, Erik; Shen, Dan; Pham, Khanh D.; Chen, Genshe
2015-05-01
Game theoretical methods have been used for spectral awareness, space situational awareness (SSA), cyber situational awareness (CSA), and Intelligence, Surveillance, and Reconnaissance situation awareness (ISA). Each of these cases, awareness is supported by sensor estimation for assessment and the situation is determined from the actions of multiple players. Game theory assumes rational actors in a defined scenario; however, variations in social, cultural and behavioral factors include the dynamic nature of the context. In a dynamic data-driven application system (DDDAS), modeling must include both the measurements but also how models are used by different actors with different priorities. In this paper, we highlight the applications of game theory by reviewing the literature to determine the current state of the art and future needs. Future developments would include building towards knowledge awareness with information technology (e.g., data aggregation, access, indexing); multiscale analysis (e.g., space, time, and frequency), and software methods (e.g., architectures, cloud computing, protocols).
Diffusion, quantum theory, and radically elementary mathematics (MN-47)
Faris, William G
2014-01-01
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in
Second order logic, set theory and foundations of mathematics
Väänänen, J.A.; Dybjer, P; Lindström, S; Palmgren, E; Sundholm, G
2012-01-01
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the
The theory of voting and equilibria in noncooperative games
DEFF Research Database (Denmark)
Sloth, Birgitte
1993-01-01
We consider the problem of modeling voting situations, seeking models and equilibrium concepts which are easier to incorporate in large sequential decision games than the models and solution concepts used by the "theory of voting." It is demonstrated that one can avoid using very refined solution...
GIS and Game Theory for Water Resource Management
Ganjali, N.; Guney, C.
2017-11-01
In this study, aspects of Game theory and its application on water resources management combined with GIS techniques are detailed. First, each term is explained and the advantages and limitations of its aspect is discussed. Then, the nature of combinations between each pair and literature on the previous studies are given. Several cases were investigated and results were magnified in order to conclude with the applicability and combination of GIS- Game Theory- Water Resources Management. It is concluded that the game theory is used relatively in limited studies of water management fields such as cost/benefit allocation among users, water allocation among trans-boundary users in water resources, water quality management, groundwater management, analysis of water policies, fair allocation of water resources development cost and some other narrow fields. Also, Decision-making in environmental projects requires consideration of trade-offs between socio-political, environmental, and economic impacts and is often complicated by various stakeholder views. Most of the literature on water allocation and conflict problems uses traditional optimization models to identify the most efficient scheme while the Game Theory, as an optimization method, combined GIS are beneficial platforms for agent based models to be used in solving Water Resources Management problems in the further studies.
Perspective of Game Theory in Education for Sustainable Development
Ahrens, A.; Zascerinska, J.
2012-01-01
The sustainable development of society has attracted a lot of research efforts. A strategic aspect to the society's evolution is introduced by the game theory (Fernandez, 2011, p. 1). The research question is as follows: how to organize the process of teaching and learning in education for sustainable development? The aim of the research is to…
A Game Theory Based Solution for Security Challenges in CRNs
Poonam; Nagpal, Chander Kumar
2018-03-01
Cognitive radio networks (CRNs) are being envisioned to drive the next generation Ad hoc wireless networks due to their ability to provide communications resilience in continuously changing environments through the use of dynamic spectrum access. Conventionally CRNs are dependent upon the information gathered by other secondary users to ensure the accuracy of spectrum sensing making them vulnerable to security attacks leading to the need of security mechanisms like cryptography and trust. However, a typical cryptography based solution is not a viable security solution for CRNs owing to their limited resources. Effectiveness of trust based approaches has always been, in question, due to credibility of secondary trust resources. Game theory with its ability to optimize in an environment of conflicting interests can be quite a suitable tool to manage an ad hoc network in the presence of autonomous selfish/malevolent/malicious and attacker nodes. The literature contains several theoretical proposals for augmenting game theory in the ad hoc networks without explicit/detailed implementation. This paper implements a game theory based solution in MATLAB-2015 to secure the CRN environment and compares the obtained results with the traditional approaches of trust and cryptography. The simulation result indicates that as the time progresses the game theory performs much better with higher throughput, lower jitter and better identification of selfish/malicious nodes.
OPTIMIZATION OF TAX REGIME USING THE INSTRUMENT OF GAME THEORY
Directory of Open Access Journals (Sweden)
Igor Yu. Pelevin
2014-01-01
Full Text Available The article is devoted to one of one possible mechanism of taxation optimization of agricultural enterprises where used the game theory. Use of this mechanism allows to apply the most optimal type of taxation that would benefit both a taxpayer and the government. In the article offered the definition of the tax storage and its possible applications.
Bridging the gap between Schumpeterian competition and evolutionary game theory
DEFF Research Database (Denmark)
Andersen, Esben Sloth
This paper suggests that the analysis of Schumpeterian competition within the Nelson-Winter model should be complemented with evolutionary game theory. This model and its limitations for density-dependent Schumpeterian strategies are presented in terms of the equations of evolutionary dynamics. F...
The Prisoner's Dilemma: Introducing Game Theory
Shaw, Doug J.; Miller, Catherine M.
2015-01-01
Since 1950, the Prisoner's Dilemma has intrigued economists and amused fans of mathematics. It presents a situation in which two players acting to their own advantage do not do as well together as two players whose actions oppose their individual interests--hence, the dilemma. Variations of the Prisoner's Dilemma have appeared in diverse…
Search theory a game theoretic perspective
2014-01-01
The first book focusing on search and rendezvous that will appeal to the computer science, mathematics and biology communities as well as non-experts Most chapters include case studies or surveys Includes a chapter on mobility in governed social networks
Mathematical theory of compressible viscous fluids analysis and numerics
Feireisl, Eduard; Pokorný, Milan
2016-01-01
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...
The limits of weak selection and large population size in evolutionary game theory.
Sample, Christine; Allen, Benjamin
2017-11-01
Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the [Formula: see text] limit, in which weak selection is applied before the large population limit, and the [Formula: see text] limit, in which the order is reversed. Formal mathematical definitions of the [Formula: see text] and [Formula: see text] limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the [Formula: see text] and [Formula: see text] limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.
Study on Mathematical Game Design Strategy based on Mobile Terminal%基于移动终端的数学游戏设计策略研究
Institute of Scientific and Technical Information of China (English)
蒋希娜; 黄心渊; 蒋蕊; 杨冷泠
2014-01-01
With the development of mobile Internet, mobile terminal products have come into the learner’s life gradually, bringing us a revival in educational games market. It also spawned a large number of mobile educational games, including mobile math games, but the quality of them is a mixed bag. In this paper, through the analysis of the status of the mobile game of mathematics, we ifnd the problems and summarize the reasons. Then, According to A. Reber’s implicit learning theory and Donald Norman’s three hierarchy theory of emotional design, we put forward the design principles and method of mobile mathematical game and try to set the mobile game design mathematical model ifnally. All these will provide the reference for the research of mobile mathematics game maker and designer.%移动互联网的发展使得移动终端产品逐步走进学习者的生活，催生大量移动教育游戏，包括不断涌现的移动数学游戏，但其质量良莠不齐。通过分析移动数学游戏现状，发现其问题，并加以归因，基于A.Reber的内隐学习理论和唐纳德·诺曼的情感化设计三层次理论，提出移动数学游戏的设计原则和方法，最终形成移动数学游戏设计模型，为移动数学游戏研究者和设计者提供参考和借鉴。
Networking of theories as a research practice in mathematics education
Bikner-Ahsbahs, Angelika
2014-01-01
How can we deal with the diversity of theories in mathematics education This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them. The book explains and illustrates what it means to network theories; it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS). A synthetic presentation of each theory and their connections shows how the activity of netw...
Defending Against Advanced Persistent Threats Using Game-Theory.
Rass, Stefan; König, Sandra; Schauer, Stefan
2017-01-01
Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical system security, since information on attacks, the current system status or the attacker's incentives is often vague, uncertain and in many cases even unavailable. Game theory is a natural approach to model the conflict between the attacker and the defender, and this work investigates a generalized class of matrix games as a risk mitigation tool for an advanced persistent threat (APT) defense. Unlike standard game and decision theory, our model is tailored to capture and handle the full uncertainty that is immanent to APTs, such as disagreement among qualitative expert risk assessments, unknown adversarial incentives and uncertainty about the current system state (in terms of how deeply the attacker may have penetrated into the system's protective shells already). Practically, game-theoretic APT models can be derived straightforwardly from topological vulnerability analysis, together with risk assessments as they are done in common risk management standards like the ISO 31000 family. Theoretically, these models come with different properties than classical game theoretic models, whose technical solution presented in this work may be of independent interest.
The mathematical theory of general relativity
Katkar, L N
2014-01-01
This book is prepared for M. Sc. Students of Mathematics and Physics. The aim of writing this book is to give the reader a feeling for the necessity and beauty of the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry. An attempt has been made to make the presentation comprehensive, rigorous and yet simple. Most calculations and transformations have been carried out in great detail. KEY FEATURE: Numerous solved examples using the well known mathematical techniques viz., the tensors and the differential forms in each chapter.
Algorithmic information theory mathematics of digital information processing
Seibt, Peter
2007-01-01
Treats the Mathematics of many important areas in digital information processing. This book covers, in a unified presentation, five topics: Data Compression, Cryptography, Sampling (Signal Theory), Error Control Codes, Data Reduction. It is useful for teachers, students and practitioners in Electronic Engineering, Computer Science and Mathematics.
Amidst Multiple Theories of Learning in Mathematics Education
Simon, Martin A.
2009-01-01
Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think…
Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective
Lewis, Gareth
2015-01-01
In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
Rhetorical ways of thinking Vygotskian theory and mathematical learning
Albert, Lillie R; Macadino, Vittoria
2012-01-01
Combining Vygotskian theory with current teaching and learning practices, this volume focuses on how the co-construction of learning models the interpretation of a mathematical situation, providing educationalists with a valuable practical methodology.
Theory-practice Dichotomy in Mathematics Teacher Education: An ...
African Journals Online (AJOL)
Theory-practice Dichotomy in Mathematics Teacher Education: An Analysis of Practicum ... Zimbabwe Journal of Educational Research ... practices in primary teacher education continue to create dichotomous gaps in this relationship.
Drummond, Aaron; Sauer, James D.
2014-01-01
Video-gaming is a common pastime among adolescents, particularly adolescent males in industrialized nations. Despite widespread suggestions that video-gaming negatively affects academic achievement, the evidence is inconclusive. We reanalyzed data from over 192,000 students in 22 countries involved in the 2009 Programme for International Student Assessment (PISA) to estimate the true effect size of frequency of videogame use on adolescent academic achievement in science, mathematics and readi...
The Impact of Video Games in Children-s Learning of Mathematics
Muhammad Ridhuan Tony Lim Abdullah; Zulqarnain Abu Bakar; Razol Mahari Ali; Ibrahima Faye; Hilmi Hasan
2012-01-01
This paper describes a research project on Year 3 primary school students in Malaysia in their use of computer-based video game to enhance learning of multiplication facts (tables) in the Mathematics subject. This study attempts to investigate whether video games could actually contribute to positive effect on children-s learning or otherwise. In conducting this study, the researchers assume a neutral stand in the investigation as an unbiased outcome of the study would render reliable respons...
Scattering theory in quantum mechanics. Physical principles and mathematical methods
International Nuclear Information System (INIS)
Amrein, W.O.; Jauch, J.M.; Sinha, K.B.
1977-01-01
A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods
Survey on nonlocal games and operator space theory
International Nuclear Information System (INIS)
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states
Survey on nonlocal games and operator space theory
Energy Technology Data Exchange (ETDEWEB)
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Practical example of game theory application for production route selection
Olender, M.; Krenczyk, D.
2017-08-01
The opportunity which opens before manufacturers on the dynamic market, especially before those from the sector of the small and medium-sized enterprises, is associated with the use of the virtual organizations concept. The planning stage of such organizations could be based on supporting decision-making tasks using the tools and formalisms taken from the game theory. In the paper the model of the virtual manufacturing network, along with the practical example of decision-making situation as two person game and the decision strategies with an analysis of calculation results are presented.
Drummond, Aaron; Sauer, James D
2014-01-01
Video-gaming is a common pastime among adolescents, particularly adolescent males in industrialized nations. Despite widespread suggestions that video-gaming negatively affects academic achievement, the evidence is inconclusive. We reanalyzed data from over 192,000 students in 22 countries involved in the 2009 Programme for International Student Assessment (PISA) to estimate the true effect size of frequency of videogame use on adolescent academic achievement in science, mathematics and reading. Contrary to claims that increased video-gaming can impair academic performance, differences in academic performance were negligible across the relative frequencies of videogame use. Videogame use had little impact on adolescent academic achievement.
Directory of Open Access Journals (Sweden)
Aaron Drummond
Full Text Available Video-gaming is a common pastime among adolescents, particularly adolescent males in industrialized nations. Despite widespread suggestions that video-gaming negatively affects academic achievement, the evidence is inconclusive. We reanalyzed data from over 192,000 students in 22 countries involved in the 2009 Programme for International Student Assessment (PISA to estimate the true effect size of frequency of videogame use on adolescent academic achievement in science, mathematics and reading. Contrary to claims that increased video-gaming can impair academic performance, differences in academic performance were negligible across the relative frequencies of videogame use. Videogame use had little impact on adolescent academic achievement.
Drummond, Aaron; Sauer, James D.
2014-01-01
Video-gaming is a common pastime among adolescents, particularly adolescent males in industrialized nations. Despite widespread suggestions that video-gaming negatively affects academic achievement, the evidence is inconclusive. We reanalyzed data from over 192,000 students in 22 countries involved in the 2009 Programme for International Student Assessment (PISA) to estimate the true effect size of frequency of videogame use on adolescent academic achievement in science, mathematics and reading. Contrary to claims that increased video-gaming can impair academic performance, differences in academic performance were negligible across the relative frequencies of videogame use. Videogame use had little impact on adolescent academic achievement. PMID:24699536
Wang, Sheng-Yuan; Chang, Shao-Chen; Hwang, Gwo-Jen; Chen, Pei-Ying
2018-01-01
In traditional teacher-centered mathematics instruction, students might show low learning motivation owing to the lack of applied contexts. Game-based learning has been recognized as a potential approach to addressing this issue; however, without proper alignment between the gaming and math-applied contexts, the benefits of game-based learning…
DEFF Research Database (Denmark)
Triantafyllou, Evangelia; Misfeldt, Morten; Timcenko, Olga
2015-01-01
In this article, we present our idea of using a game engine (Unity) to teach Media Technology students mathematics-related concepts. In order to observe how the introduction of a technological tool, namely the game engine, changes the practices in mathematical work, we adopted the anthropological...
Improving Preschoolers' Theory of Mind Skills with Digital Games: A Training Study
Nikolayev, Mariya
2015-01-01
This single-subject research study examined functional relation between digital games enriched with voice-overs and theory of mind (ToM) when game play was either followed or not followed by a discussion focused on the game's content. The study employed multiple baseline design across participants to evaluate the effects of games with mental state…
Game theory in models of pedestrian room evacuation
Bouzat, S.; Kuperman, M. N.
2014-03-01
We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.
Chimpanzee choice rates in competitive games match equilibrium game theory predictions.
Martin, Christopher Flynn; Bhui, Rahul; Bossaerts, Peter; Matsuzawa, Tetsuro; Camerer, Colin
2014-06-05
The capacity for strategic thinking about the payoff-relevant actions of conspecifics is not well understood across species. We use game theory to make predictions about choices and temporal dynamics in three abstract competitive situations with chimpanzee participants. Frequencies of chimpanzee choices are extremely close to equilibrium (accurate-guessing) predictions, and shift as payoffs change, just as equilibrium theory predicts. The chimpanzee choices are also closer to the equilibrium prediction, and more responsive to past history and payoff changes, than two samples of human choices from experiments in which humans were also initially uninformed about opponent payoffs and could not communicate verbally. The results are consistent with a tentative interpretation of game theory as explaining evolved behavior, with the additional hypothesis that chimpanzees may retain or practice a specialized capacity to adjust strategy choice during competition to perform at least as well as, or better than, humans have.
Fu, Guifang
2017-03-01
Qian Wang et al. have written an interesting article to propose a modeling framework named epiGame in this issue of Physics of Life Reviews [1]. The epiGame framework models how the methylation state of paternal and maternal genomes regulates the embryogenesis as an ecological system in which two highly distinct and specialized gametes coordinate through either cooperation or competition, or both, to maximize the fitness of embryos. Qian Wang et al. also provide solid simulation studies and real data analysis to validate the correctness of their epiGame framework. The importance of embryo development and fertility mechanism cannot be overemphasized, hence, I think that the present review by Qian Wang et al. will stand as a useful modeling guide for practicing biologists or researchers in fertility health to quantify how sperms and oocytes interact through epigenetic process to determine embryo development. In addition, it will serve as a source of many important references to work in the reproductive biology field.
The Mathematical Theory of Multifocal Lenses
Institute of Scientific and Technical Information of China (English)
Jacob RUBINSTEIN
2017-01-01
This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them.In particular,it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces.A key role is played by Hamilton's eikonal functions.It is shown that these functions capture all the information on the local blur and distortion created by the lenses.Along the way,formulas for computing the eikonal functions are derived.Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.
Handbook of Game Theory and Industrial Organization, Volume I: Theory. An Introduction
Corchon, Luis; Marini, Marco A.
2017-01-01
We introduce here the first volume of Handbook of Game Theory and Industrial Organization: Theory, by L. C. Corchón and M. A. Marini (eds.), Edward Elgar, Cheltenam, UK and Northampton, MA, by describing its main aim and its basic structure.
On the inclusion of macroscopic theory in Monte Carlo simulation using game theory
International Nuclear Information System (INIS)
Tatarkiewicz, J.
1980-01-01
This paper presents the inclusion of macroscopic damage theory into Monte Carlo particle-range simulation using game theory. A new computer code called RADDI was developed on the basis of this inclusion. Results of Monte Carlo damage simulation after 6.3 MeV proton bombardment of silicon are compared with experimental data of Bulgakov et al. (orig.)
Forthcoming Issue on Game Theory and Political Economy
Directory of Open Access Journals (Sweden)
William D. Ferguson
2013-09-01
Full Text Available Game theory offers a rigorous set of concepts, relationships, and models that invite myriad applications to problems of political economy. Indeed, game theory can serve as a fundamental modeling technique that can bridge microfoundations of political and economic exchanges, with developmental processes and macro implications related to growth and distribution. Applications can range from localized interactions within workplaces, firms, political organizations, and community groups; to intermediate-level market, industry, community, or inter-organizational transactions; to encompassing national, regional, population, or global interactions. At any of these levels, game models can illustrate strategic responses of economic or political actors (individuals or organizations to specifiable conditions concerning any or all of the following: prevailing social context—notably informal institutions (such as social norms and formal institutions (such as mutually understood laws and regulations; available information (complete or not; accessible or strategically manipulated; agents’ motivations (material and/or social; and even levels of rationality—substantive (full cognition or bounded (limited cognition. Applicable models may operate on the basis of given institutional context and preference orientations or may explore associated developmental processes, including adaptive social learning. Of particular interest are representations of one or more of the myriad social dilemmas (or collective-action problems that inhabit political economy, associated exercises or distributions of power, and/or representations of potential resolutions to such dilemmas—perhaps with policy implications. Accordingly, this forthcoming issue of Economies seeks game-theoretic models based on classical, evolutionary, behavioral, or epistemic game theory that can be applied to one or more problems in political economy.
Science and mathematics teaching through local games in preschools of Botswana
Directory of Open Access Journals (Sweden)
Kabita Bose
2016-11-01
Full Text Available This article presents a study regarding preschool teachers’ skills and competencies in teaching science and mathematics. The aim of the project was twofold; one to find out the preschool teachers’ knowledge about mathematics and science concepts and then to develop support material to empower them with skills and competencies to teach these concepts in preschools. A qualitative approach was adopted, and a case study method was used. Data were collected through two workshops and focus group discussions with preschool teachers. The study revealed that the preschool teachers had content knowledge, but lacked pedagogical knowledge that is crucial in teaching of preschool children, and they provided science and mathematics experiences in preschools scarcely. A resource book of 33 local games and rhymes thus was developed as a support material to empower the teachers with skills and competencies to use play to teach science and mathematics in preschools. The resource book developed consists of 33 local games/rhymes and is packaged with the games’ illustrations, steps and rules followed in the games, science and mathematics concepts and competencies that could be taught to children, along with probing questions that would help in teaching of science and mathematics concepts to children.
Probability elements of the mathematical theory
Heathcote, C R
2000-01-01
Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.
New Mayan Hieroglyphics Support For A Mathematical Theory of Civilizations
Blaha, S
2002-01-01
Newly found Mayan hieroglyphics (at Dos Pilas, Guatemala) that describe a series of wars between Mayan "superpowers" Tikal and Calakmul appear to support a new mathematical theory of civilizations. Major events in the history of Teotihuacan (near Mexico City) in Mayan times also are consistent with the predictions of this theory.
Directory of Open Access Journals (Sweden)
Joško Sindik
2008-06-01
Full Text Available A mathematical method of decision-making in which a competitive or cooperative situation is analyzed to determine the optimal course of action for an interested “player” is often called game theory. Game theory has very broad application in different sciences. Team sports tactical performance is considered from the aspects of data processing theory and the phenomenon of selective attention, as well as from the game theory. Team sports tactical performance is an asymmetric, sequential (of imperfect information, non-zero-sum game. In decision making, predictability in team sports is in fact bargaining, and the player has to use a mixed strategy for choosing option with highest expected utility. Player could choose a trembling hand equilibrium, to eliminate imperfect equilibrium. Strategic dominance conceipt can explain that a player could choose strategy which dominates between other possible strategies, and/or could be led by “team reasoning”, too. In this article, the level of predictability of the most frequent tactical performance of one player in a team sport game is considered, reflecting outcomes both for the same team’s tactical performance (co-players in one player’s team, as well as for the opponent team’s tactical performance. Four different possible situations during team sport competition could lead to considering utilities of one player’s specific decisions.
THE THEORY OF THE FIRM AND THE EVOLUTIONARY GAMES
Directory of Open Access Journals (Sweden)
Sirghi Nicoleta
2013-07-01
Full Text Available The neoclassical theory of the firm deals with the pattern of perfect competition, within which the perfect information available to economic agents provides instant allocation of production factors and access to economic goods. The Austrian School (C. Menger, L. von Mises, Hayek, etc. supported the idea of minimal state intervention on the markets, bringing important conceptual developments on the theory of the firm. Hirschleifer (1982 put forward the model of social and institutional functioning, arguing that the game theory is able to predict the outcome of the collective behavior and the human characteristics necessary for building the respective institutions.The evolutionary theory provides the firm and the entrepreneur the recognition of the functions of innovation, of generating and exploiting information and of organizing and coordinating production. The evolutionary perspective of the firm assumes the existence of a body of knowledge that is acquired through and builds up the organizational memory, subsequently found in routines, all choices being made based on these routines (Nelson and Winter, 2002. The evolution of the firm is considered to be similar to natural selection, but unlike the classic market selection, the evolutionists suggest the existence of a plurality of selection media. The present research is structured as follows: a brief introduction into the theories of the firm, the second part of the paper analyzes the theories of the firm from an institutional, neo-institutional and evolutionary perspective. In the third part of the paper the evolutionary games are described and analyzed from the evolutionary perspective of the firm. The last part of the paper represents a study of the “hawk-dove” game dynamic replicator. The final conclusions of the paper show that the evolutionary theory brings valuable contributions to the foundation of explanations regarding economic phenomena, indicating new directions for advanced
Einstein's Theory A Rigorous Introduction for the Mathematically Untrained
Grøn, Øyvind
2011-01-01
This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and genera...
Ensemble method: Community detection based on game theory
Zhang, Xia; Xia, Zhengyou; Xu, Shengwu; Wang, J. D.
2014-08-01
Timely and cost-effective analytics over social network has emerged as a key ingredient for success in many businesses and government endeavors. Community detection is an active research area of relevance to analyze online social network. The problem of selecting a particular community detection algorithm is crucial if the aim is to unveil the community structure of a network. The choice of a given methodology could affect the outcome of the experiments because different algorithms have different advantages and depend on tuning specific parameters. In this paper, we propose a community division model based on the notion of game theory, which can combine advantages of previous algorithms effectively to get a better community classification result. By making experiments on some standard dataset, it verifies that our community detection model based on game theory is valid and better.
The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.
Lehtonen, Jussi
2018-01-01
A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.
Using game theory to analyze green stormwater infrastructure implementation policies
William, R. K.; Garg, J.; Stillwell, A. S.
2017-12-01
While green stormwater infrastructure is a useful approach in addressing multiple challenges facing the urban environment, little consensus exists on how to best incentivize its adoption by private landowners. Game theory, a field of study designed to model conflict and cooperation between two or more agents, is well-suited to address this policy question. We used a cooperative game theory framework to analyze the impacts of three different policy approaches frequently used to incentivize the uptake of green infrastructure by private landowners: municipal regulation, direct grants, and stormwater fees. The results indicate that municipal regulation leads to the greatest environmental benefits; however, the choice of "best" regulatory approach is dependent on a variety of different factors including political and financial considerations. Policy impacts are also highly dependent on agents' spatial positions within the stormwater network. This finding leads to important questions of social equity and environmental justice.
A game theory analysis of green infrastructure stormwater management policies
William, Reshmina; Garg, Jugal; Stillwell, Ashlynn S.
2017-09-01
Green stormwater infrastructure has been demonstrated as an innovative water resources management approach that addresses multiple challenges facing urban environments. However, there is little consensus on what policy strategies can be used to best incentivize green infrastructure adoption by private landowners. Game theory, an analysis framework that has historically been under-utilized within the context of stormwater management, is uniquely suited to address this policy question. We used a cooperative game theory framework to investigate the potential impacts of different policy strategies used to incentivize green infrastructure installation. The results indicate that municipal regulation leads to the greatest reduction in pollutant loading. However, the choice of the "best" regulatory approach will depend on a variety of different factors including politics and financial considerations. Large, downstream agents have a disproportionate share of bargaining power. Results also reveal that policy impacts are highly dependent on agents' spatial position within the stormwater network, leading to important questions of social equity and environmental justice.
Kim, Heesung; Ke, Fengfeng
2017-01-01
This experimental study was intended to examine whether the integration of game characteristics in the OpenSimulator-supported virtual reality (VR) learning environment can improve mathematical achievement for elementary school students. In this pre- and posttest experimental comparison study, data were collected from 132 fourth graders through an…
Computer Mathematics Games and Conditions for Enhancing Young Children's Learning of Number Sense
Kermani, Hengameh
2017-01-01
Purpose: The present study was designed to examine whether mathematics computer games improved young children's learning of number sense under three different conditions: when used individually, with a peer, and with teacher facilitation. Methodology: This study utilized a mixed methodology, collecting both quantitative and qualitative data. A…
Mathematics Achievement with Digital Game-Based Learning in High School Algebra 1 Classes
Ferguson, Terri Lynn Kurley
2014-01-01
This study examined the impact of digital game-based learning (DGBL) on mathematics achievement in a rural high school setting in North Carolina. A causal comparative research design was used in this study to collect data to determine the effectiveness of DGBL in high school Algebra 1 classes. Data were collected from the North Carolina…
Pre-Service Teacher Training on Game-Enhanced Mathematics Teaching and Learning
Meletiou-Mavrotheris, Maria; Prodromou, Theodosia
2016-01-01
The paper reports the main insights from a study aimed at equipping a group of pre-service teachers with the knowledge, skills, and practical experience required to effectively integrate educational games within the mathematics curriculum. An instructional intervention based on the Technological Pedagogical and Content Knowledge framework was…
Longitudinal Data on the Effectiveness of Mathematics Mini-Games in Primary Education
Bakker, Marjoke; Van den Heuvel-Panhuizen, Marja; Robitzsch, Alexander
2015-01-01
This paper describes a dataset consisting of longitudinal data gathered in the BRXXX project. The aim of the project was to investigate the effectiveness of online mathematics mini-games in enhancing primary school students' multiplicative reasoning ability (multiplication and division). The dataset includes data of 719 students from 35 primary…
Bakker, Marjoke; Van den Heuvel-Panhuizen, M.; Robitzsch, Alexander
2015-01-01
This study used a large-scale cluster randomized longitudinal experiment (N=719; 35schools) to investigate the effects of online mathematics mini-games on primary school students' multiplicative reasoning ability. The experiment included four conditions: playing at school, integrated in a lesson
Yavuz, Ahmet
2015-01-01
This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…
The bounds of reason game theory and the unification of the behavioral sciences
Gintis, Herbert
2014-01-01
Game theory is central to understanding human behavior and relevant to all of the behavioral sciences-from biology and economics, to anthropology and political science. However, as The Bounds of Reason demonstrates, game theory alone cannot fully explain human behavior and should instead complement other key concepts championed by the behavioral disciplines. Herbert Gintis shows that just as game theory without broader social theory is merely technical bravado, so social theory without game theory is a handicapped enterprise. This edition has been thoroughly revised and updated. Reinvigorati
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
Potential games and interactive decisions with multiple criteria
Voorneveld, M.
1999-01-01
Game theory is a mathematical theory for analyzing strategic interaction between decision makers. This thesis covers two game-theoretic topics. The first part of this thesis deals with potential games: noncooperative games in which the information about the goals of the separate players that is
Advances in dynamic and mean field games theory, applications, and numerical methods
Viscolani, Bruno
2017-01-01
This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...
A review of game theory approach to cyber security risk management
African Journals Online (AJOL)
A review of game theory approach to cyber security risk management. ... This paper presents a review of game theoretic-based model for cyber security risk management. Specifically, issues on ... AJOL African Journals Online. HOW TO USE ...
Mitigating Free Riding in Peer-To-Peer Networks: Game Theory ...
African Journals Online (AJOL)
Mitigating Free Riding in Peer-To-Peer Networks: Game Theory Approach. ... In this paper, we model the interactions between peers as a modified gift giving game and proposed an utility exchange incentive ... AJOL African Journals Online.
Mathematical methods of many-body quantum field theory
Lehmann, Detlef
2004-01-01
Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...
Mathematical theory of elasticity of quasicrystals and its applications
Fan, Tian-You
2016-01-01
This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket m...
Synthesis of robust nonlinear autopilots using differential game theory
Menon, P. K. A.
1991-01-01
A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.
Analysis on stability of strategic alliance: A game theory perspective
Institute of Scientific and Technical Information of China (English)
CHEN Fei-qiong; FAN Liang-cong
2006-01-01
Strategic alliance has suffered much instabilities since its first implementation. Scholars have carried out many embedded, precise and comprehensive researches from both theory and empiricism. Here we try to find certain stable solutions by employing game theory, in an attempt to construct theoretical bases for strategic alliance, which people called "one of the most important organizational innovation in the end of the 20th century" (Shi, 2001), to exploit its advantages in the process of globalization. Finally, this article puts forward some advices for its success.
Towards a mathematical theory of meaningful communication
Corominas-Murtra, Bernat; Fortuny, Jordi; Solé, Ricard V.
2014-04-01
Meaning has been left outside most theoretical approaches to information in biology. Functional responses based on an appropriate interpretation of signals have been replaced by a probabilistic description of correlations between emitted and received symbols. This assumption leads to potential paradoxes, such as the presence of a maximum information associated to a channel that creates completely wrong interpretations of the signals. Game-theoretic models of language evolution and other studies considering embodied communicating agents show that the correct (meaningful) match resulting from agent-agent exchanges is always achieved and natural systems obviously solve the problem correctly. Inspired by the concept of duality of the communicative sign stated by the swiss linguist Ferdinand de Saussure, here we present a complete description of the minimal system necessary to measure the amount of information that is consistently decoded. Several consequences of our developments are investigated, such as the uselessness of a certain amount of information properly transmitted for communication among autonomous agents.
Trinter, Christine P.; Brighton, Catherine M.; Moon, Tonya R.
2015-01-01
Primary grade students enter the mathematics classroom with a range of differences including students' mathematical readiness, mathematical conceptions, interests, and learning profiles. Addressing the learning needs of students is not a trivial task, but accounting for these needs is essential for supporting students as they continually work…
Mathematical Theory of Dispersion-Managed Optical Solitons
Biswas, Anjan; Edwards, Matthew
2010-01-01
"Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research. The book is intended for researchers and graduate students in applied mathematics, physics and engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics. Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M Univ...
Probabilistic theory of mean field games with applications
Carmona, René
2018-01-01
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...
Games in the Arctic: applying game theory insights to Arctic challenges
Directory of Open Access Journals (Sweden)
Scott Cole
2014-08-01
Full Text Available We illustrate the benefits of game theoretic analysis for assisting decision-makers in resolving conflicts and other challenges in a rapidly evolving region. We review a series of salient Arctic issues with global implications—managing open-access fisheries, opening Arctic areas for resource extraction and ensuring effective environmental regulation for natural resource extraction—and provide insights to help reach socially preferred outcomes. We provide an overview of game theoretic analysis in layman's terms, explaining how game theory can help researchers and decision-makers to better understand conflicts, and how to identify the need for, and improve the design of, policy interventions. We believe that game theoretic tools are particularly useful in a region with a diverse set of players ranging from countries to firms to individuals. We argue that the Arctic Council should take a more active governing role in the region by, for example, dispersing information to “players” in order to alleviate conflicts regarding the management of common-pool resources such as open-access fisheries and natural resource extraction. We also identify side payments—that is, monetary or in-kind compensation from one party of a conflict to another—as a key mechanism for reaching a more biologically, culturally and economically sustainable Arctic future. By emphasizing the practical insights generated from an academic discipline, we present game theory as an influential tool in shaping the future of the Arctic—for individual researchers, for inter-disciplinary research and for policy-makers themselves.
Nonconvex Model of Material Growth: Mathematical Theory
Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.
2018-06-01
The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.
Mathematical Theories of Interaction with Oracles
2013-10-01
have made a lasting impact on my mathematical perspective. I am grateful for the wonderful and stimulating discussion I had with Alan Frieze on...Otherwise, by Theorem 7.1, with probability at least 1−ε/2, we have ‖πθ⋆ −πθ̂(t−1)θ⋆‖ ≤ R(t−1, ε/2). On this event, ifR (t−1, ε/2) ≤ ε/8, then by a triangle... impact on how much benefit we gain from transfer learning when we are faced with only a finite sequence of learning problems. As such, it is certainly
Should the model for risk-informed regulation be game theory rather than decision theory?
Bier, Vicki M; Lin, Shi-Woei
2013-02-01
Risk analysts frequently view the regulation of risks as being largely a matter of decision theory. According to this view, risk analysis methods provide information on the likelihood and severity of various possible outcomes; this information should then be assessed using a decision-theoretic approach (such as cost/benefit analysis) to determine whether the risks are acceptable, and whether additional regulation is warranted. However, this view ignores the fact that in many industries (particularly industries that are technologically sophisticated and employ specialized risk and safety experts), risk analyses may be done by regulated firms, not by the regulator. Moreover, those firms may have more knowledge about the levels of safety at their own facilities than the regulator does. This creates a situation in which the regulated firm has both the opportunity-and often also the motive-to provide inaccurate (in particular, favorably biased) risk information to the regulator, and hence the regulator has reason to doubt the accuracy of the risk information provided by regulated parties. Researchers have argued that decision theory is capable of dealing with many such strategic interactions as well as game theory can. This is especially true in two-player, two-stage games in which the follower has a unique best strategy in response to the leader's strategy, as appears to be the case in the situation analyzed in this article. However, even in such cases, we agree with Cox that game-theoretic methods and concepts can still be useful. In particular, the tools of mechanism design, and especially the revelation principle, can simplify the analysis of such games because the revelation principle provides rigorous assurance that it is sufficient to analyze only games in which licensees truthfully report their risk levels, making the problem more manageable. Without that, it would generally be necessary to consider much more complicated forms of strategic behavior (including
Mathematical Systems Theory : from Behaviors to Nonlinear Control
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
A course in mathematical statistics and large sample theory
Bhattacharya, Rabi; Patrangenaru, Victor
2016-01-01
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics — parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods. Large Sample theory with many worked examples, numerical calculations, and simulations to illustrate theory Appendices provide ready access to a number of standard results, with many proofs Solutions given to a number of selected exercises from Part I Part II exercises with ...
Game Theory Meets Wireless Sensor Networks Security Requirements and Threats Mitigation: A Survey.
Abdalzaher, Mohamed S; Seddik, Karim; Elsabrouty, Maha; Muta, Osamu; Furukawa, Hiroshi; Abdel-Rahman, Adel
2016-06-29
We present a study of using game theory for protecting wireless sensor networks (WSNs) from selfish behavior or malicious nodes. Due to scalability, low complexity and disseminated nature of WSNs, malicious attacks can be modeled effectively using game theory. In this study, we survey the different game-theoretic defense strategies for WSNs. We present a taxonomy of the game theory approaches based on the nature of the attack, whether it is caused by an external attacker or it is the result of an internal node acting selfishly or maliciously. We also present a general trust model using game theory for decision making. We, finally, identify the significant role of evolutionary games for WSNs security against intelligent attacks; then, we list several prospect applications of game theory to enhance the data trustworthiness and node cooperation in different WSNs.
Game Theory Meets Wireless Sensor Networks Security Requirements and Threats Mitigation: A Survey
Directory of Open Access Journals (Sweden)
Mohamed S. Abdalzaher
2016-06-01
Full Text Available We present a study of using game theory for protecting wireless sensor networks (WSNs from selfish behavior or malicious nodes. Due to scalability, low complexity and disseminated nature of WSNs, malicious attacks can be modeled effectively using game theory. In this study, we survey the different game-theoretic defense strategies for WSNs. We present a taxonomy of the game theory approaches based on the nature of the attack, whether it is caused by an external attacker or it is the result of an internal node acting selfishly or maliciously. We also present a general trust model using game theory for decision making. We, finally, identify the significant role of evolutionary games for WSNs security against intelligent attacks; then, we list several prospect applications of game theory to enhance the data trustworthiness and node cooperation in different WSNs.
Ku, Oskar; Chen, Sherry Y.; Wu, Denise H.; Lao, Andrew C. C.; Chan, Tak-Wai
2014-01-01
Many students possess low confidence toward learning mathematics, which, in turn, may lead them to give up pursuing more mathematics knowledge. Recently, game-based learning (GBL) is regarded as a potential means in improving students' confidence. Thus, this study tried to promote students' confidence toward mathematics by using GBL. In addition,…
Game Theory and Risk-Based Levee System Design
Hui, R.; Lund, J. R.; Madani, K.
2014-12-01
Risk-based analysis has been developed for optimal levee design for economic efficiency. Along many rivers, two levees on opposite riverbanks act as a simple levee system. Being rational and self-interested, land owners on each river bank would tend to independently optimize their levees with risk-based analysis, resulting in a Pareto-inefficient levee system design from the social planner's perspective. Game theory is applied in this study to analyze decision making process in a simple levee system in which the land owners on each river bank develop their design strategies using risk-based economic optimization. For each land owner, the annual expected total cost includes expected annual damage cost and annualized construction cost. The non-cooperative Nash equilibrium is identified and compared to the social planner's optimal distribution of flood risk and damage cost throughout the system which results in the minimum total flood cost for the system. The social planner's optimal solution is not feasible without appropriate level of compensation for the transferred flood risk to guarantee and improve conditions for all parties. Therefore, cooperative game theory is then employed to develop an economically optimal design that can be implemented in practice. By examining the game in the reversible and irreversible decision making modes, the cost of decision making myopia is calculated to underline the significance of considering the externalities and evolution path of dynamic water resource problems for optimal decision making.
Storming a Citadel: Mathematical Theory and Experimental Practice
Sichau, Christian
2006-09-01
Based upon a comparison of the viscosity experiments of James Clerk Maxwell (1831 1879) and Oskar Emil Meyer (1834 1909) in the 1860s, I argue that mathematical theory plays a significant role in both aspects of experimental practice, the design and construction of an experimental apparatus and the transformation of the observed experimental data into the value of a physical quantity. I argue further that Maxwell’s and Meyer’s evaluation of each other’s theoretical and experimental work depended significantly on the mathematical tools they employed in their theories.
The mathematical theory of signal processing and compression-designs
Feria, Erlan H.
2006-05-01
The mathematical theory of signal processing, named processor coding, will be shown to inherently arise as the computational time dual of Shannon's mathematical theory of communication which is also known as source coding. Source coding is concerned with signal source memory space compression while processor coding deals with signal processor computational time compression. Their combination is named compression-designs and referred as Conde in short. A compelling and pedagogically appealing diagram will be discussed highlighting Conde's remarkable successful application to real-world knowledge-aided (KA) airborne moving target indicator (AMTI) radar.
Matrix Mathematics Theory, Facts, and Formulas (Second Edition)
Bernstein, Dennis S
2011-01-01
When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat
International Summer School on Mathematical Systems Theory and Economics
Szegö, G
1969-01-01
The International Summer School on Mathematical Systems Theory and Economics was held at the Villa Monastero in Varenna, Italy, from June 1 through June 12, 1967. The objective of this Summer School was to review the state of the art and the prospects for the application of the mathematical theory of systems to the study and the solution of economic problems. Particular emphasis was given to the use of the mathematical theory of control for the solution of problems in economics. It was felt that the publication of a volume collecting most of the lectures given at the school would show the current status of the application of these methods. The papers are organized into four sections arranged into two volumes: basic theories and optimal control of economic systems which appear in the first volume, and special mathematical problems and special applications which are contained in the second volume. Within each section the papers follow in alphabetical order by author. The seven papers on basic theories are a rat...
Optimal threshold estimation for binary classifiers using game theory.
Sanchez, Ignacio Enrique
2016-01-01
Many bioinformatics algorithms can be understood as binary classifiers. They are usually compared using the area under the receiver operating characteristic ( ROC ) curve. On the other hand, choosing the best threshold for practical use is a complex task, due to uncertain and context-dependent skews in the abundance of positives in nature and in the yields/costs for correct/incorrect classification. We argue that considering a classifier as a player in a zero-sum game allows us to use the minimax principle from game theory to determine the optimal operating point. The proposed classifier threshold corresponds to the intersection between the ROC curve and the descending diagonal in ROC space and yields a minimax accuracy of 1-FPR. Our proposal can be readily implemented in practice, and reveals that the empirical condition for threshold estimation of "specificity equals sensitivity" maximizes robustness against uncertainties in the abundance of positives in nature and classification costs.
Statistical physics and computational methods for evolutionary game theory
Javarone, Marco Alberto
2018-01-01
This book presents an introduction to Evolutionary Game Theory (EGT) which is an emerging field in the area of complex systems attracting the attention of researchers from disparate scientific communities. EGT allows one to represent and study several complex phenomena, such as the emergence of cooperation in social systems, the role of conformity in shaping the equilibrium of a population, and the dynamics in biological and ecological systems. Since EGT models belong to the area of complex systems, statistical physics constitutes a fundamental ingredient for investigating their behavior. At the same time, the complexity of some EGT models, such as those realized by means of agent-based methods, often require the implementation of numerical simulations. Therefore, beyond providing an introduction to EGT, this book gives a brief overview of the main statistical physics tools (such as phase transitions and the Ising model) and computational strategies for simulating evolutionary games (such as Monte Carlo algor...
Mathematics Learning by Programming in a Game Engine
DEFF Research Database (Denmark)
Triantafyllou, Evangelia; Timcenko, Olga; Misfeldt, Morten
2017-01-01
This paper emerges from our research focusing on mathematics education in trans-disciplinary engineering programs and presents a case study in such an engineering discipline, namely the Media Technology program at Aalborg University Copenhagen, Denmark. In this case study, we substituted traditio...
Digital game based learning: A new method in teaching and learning mathematics
Hussain, Sayed Yusoff bin Syed; Hoe, Tan Wee; Idris, Muhammad Zaffwan bin
2017-05-01
Digital game-based learning (DGBL) had been regarded as a sound learning strategy in raising pupils' willingness and interest in many disciplines. Normally, video and digital games are used in the teaching and learning mathematics. based on literature, digital games have proven its capability in making pupils motivated and are more likely to contribute to effective learning mathematics. Hence this research aims to construct a DGBL in the teaching of Mathematics for Year 1 pupils. Then, a quasi-experimental study was carried out in a school located in Gua Musang, Kelantan, involving 39 pupils. Specifically, this article tests the effectiveness of the use of DGBL in the teaching of the topic Addition of Less than 100 on pupil's achievement. This research employed a quasi-experiment, Pre and Post Test of Non-equivalent Control Group design. The data were analysed using the Nonparametric test namely the Mann-Whitney U. The research finding shows the use of the DGBL could increase the pupils' achievement in the topic of Addition of Less than 100. In practice, this research indicates that the DBGL can utilized as an alternative reference strategy for Mathematics teacher.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Ciocci, Argante; Viti, Andrea; Terzi, Alberto; Bertolaccini, Luca
2015-11-01
Game theory is a formal way to analyze the interactions among groups of subjects who behave each other. It has historically been of great interest in the economic fields in which decisions are made in a competitive environment. Game theory has fascinating potential if applied in the medical science. Few papers have been written about the application of game theory in surgery. The majority of scenarios of game theory in surgery fall into two main groups: cooperative and no cooperative games.
Gummerum, Michaela; Hanoch, Yaniv; Keller, Monika
2008-01-01
Game theory has been one of the most prominent theories in the social sciences, influencing diverse academic disciplines such as anthropology, biology, economics, and political science. In recent years, economists have employed game theory to investigate behaviors relating to fairness, reciprocity, and trust. Surprisingly, this research has not…
Orton, Robert E.
1988-01-01
The ideas of Kuhn and Lakatos are used to study four issues in mathematics education related to values, units of analysis, theory of mind, and nature of mathematical entities. The goal is to determine whether differences between the assumptions are best understood in Kuhnian or Lakatosian terms. (MNS)
Designing Opportunities to Learn Mathematics Theory-Building Practices
Bass, Hyman
2017-01-01
Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…
Aspects of Theories, Frameworks and Paradigms in Mathematics Education Research
Stoilescu, Dorian
2016-01-01
This article discusses major theoretical debates and paradigms from the last decades in general education and their specific influences in mathematics education contexts. Behaviourism, cognitive science, constructivism, situated cognition, critical theory, place-based learning, postmodernism and poststructuralism and their significant aspects in…
Anku, Sitsofe E.
1997-09-01
Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
网络经济的博弈论分析%Analysis of the Game Theory in Network Economy
Institute of Scientific and Technical Information of China (English)
王玉
2001-01-01
Based on the non-asymmetrical information game theory, this paper analyzes the trust-agency mechanism in network economy, the change of the rules of the game and the strategies of the game in the network environment.
Multispectral iris recognition based on group selection and game theory
Ahmad, Foysal; Roy, Kaushik
2017-05-01
A commercially available iris recognition system uses only a narrow band of the near infrared spectrum (700-900 nm) while iris images captured in the wide range of 405 nm to 1550 nm offer potential benefits to enhance recognition performance of an iris biometric system. The novelty of this research is that a group selection algorithm based on coalition game theory is explored to select the best patch subsets. In this algorithm, patches are divided into several groups based on their maximum contribution in different groups. Shapley values are used to evaluate the contribution of patches in different groups. Results show that this group selection based iris recognition
[The problem of divisions, wagers, and game theory].
Cléro, Jean-Pierre
2011-01-01
This article looks at the "problem of the divisions" - a dialogue between two persons or more - to bring out its structure, in which religious and ethical elements are intermingled. It then offers a reevaluation of the argument of the wager, which is seen here as a sort of prefiguration of game theory rather than as the solution to a problem of probabilities. Although their correspondence suggests that Fermat and Pascal believed they were offering a solution to the same problem, they were not - as written by Fermat, the problem of divisions is a problem of probabilities, but ultimately Fermat did not solve the same problem as Pascal.
Directory of Open Access Journals (Sweden)
Itamar Miranda da Silva
2011-06-01
Full Text Available This paper discusses the possibilities of articulation of theory-and-practice in the teaching, by means of critical mathematics education as a proposal for the teacher facing the challenges of daily life in the classroom. The discussion is based on the literature through which was estudied and analyzed several books, articles and dissertations on the subject, as well as our experiences and reflections resulting from the process of teacher education we experienced. From the readings and analysis was possible to construct a teaching proposal that suggests to address critical mathematics education as an alternative link between theory and practice and to assign to the teaching of mathematics a greater dynamism, with the prospect of developing knowledge and pedagogical practices that contribute to a broader training, which prepares for citizenship and for being critical students and teachers in the training process. Conjectures were raised about possible contributions of critical mathematics education as a differentiated alternative as opposed to reproductivist teaching. We believe therefore that this article could help with the reflections on the importance of mathematics education in teacher education which enables the realization that beyond disciplinary knowledge (content, are necessary pedagogical knowledge, curriculum and experiential to address the problems that relate to the teaching of mathematics
Game Theory Paradigm: A New Tool for Investigating Social Dysfunction in Major Depressive Disorders.
Wang, Yun; Yang, Liu-Qing; Li, Shu; Zhou, Yuan
2015-01-01
Social dysfunction is a prominent source of distress and disability in patients with major depressive disorder (MDD) but is commonly omitted from current clinical studies, although some researchers propose an evolutionary strategy to understand these negative outcomes. Limited knowledge about the neural basis of social dysfunction in MDD results from traditional paradigms, which lack insights into social interactions. Game theoretical modeling offers a new tool for investigating social-interaction impairments in neuropsychiatric disorders. This review first introduces three widely used games from game theory and the major behavioral and neuroimaging findings obtained using these games in healthy populations. We also address the factors that modulate behaviors in games and their neural bases. We then summarize the current findings obtained by using these games in depressed patients and discuss the clinical implications of these abnormal game behaviors. Finally, we briefly discuss future prospects that may further elucidate the clinical use of a game theory paradigm in MDD.
“I am a rogue night elf”: Avatars, gaming and The Big Bang Theory
Directory of Open Access Journals (Sweden)
Theo Plothe
2014-03-01
Full Text Available CBS’s The Big Bang Theory (TBBT frequently exhibits elements of video games and gaming culture. The author uses subculture theory to consider the representation of video games, gamers, and their avatars within popular culture. This paper investigates the representation of avatars within the characterization of gaming subculture on the TBBT. The author performed a content analysis of the program’s six seasons, examining the relationship between the show’s video game playing characters and their avatars. This investigation found that almost half of the scenes that contained video gaming activities contained some aspect of avatars. TBBT reifies gaming as a subculture through the relationship between the characters and their avatars. Examining the representation of these relationships is essential to understanding the representation of the gaming subculture in the mass media and within culture at large.
Game theory paradigm: a new tool for investigating social dysfunction in major depressive disorders
Directory of Open Access Journals (Sweden)
Yun eWang
2015-09-01
Full Text Available Social dysfunction is a prominent source of distress and disability in patients with major depressive disorder (MDD but is commonly omitted from current clinical studies, although some researchers propose an evolutionary strategy to understand these negative outcomes. Limited knowledge about the neural basis of social dysfunction in MDD results from traditional paradigms, which lack insights into social interactions. Game theoretical modelling offers a new tool for investigating social interaction impairments in neuropsychiatric disorders. This review first introduces three widely-used games from game theory and the major behavioral and neuroimaging findings obtained using these games in healthy populations. We also address the factors that modulate behaviors in games and their neural bases. We then summarize the current findings obtained by using these games in depressed patients and discuss the clinical implications of these abnormal game behaviors. Finally, we briefly discuss future prospects that may further elucidate the clinical use of a game theory paradigm in MDD.
Game Theory Paradigm: A New Tool for Investigating Social Dysfunction in Major Depressive Disorders
Wang, Yun; Yang, Liu-Qing; Li, Shu; Zhou, Yuan
2015-01-01
Social dysfunction is a prominent source of distress and disability in patients with major depressive disorder (MDD) but is commonly omitted from current clinical studies, although some researchers propose an evolutionary strategy to understand these negative outcomes. Limited knowledge about the neural basis of social dysfunction in MDD results from traditional paradigms, which lack insights into social interactions. Game theoretical modeling offers a new tool for investigating social-interaction impairments in neuropsychiatric disorders. This review first introduces three widely used games from game theory and the major behavioral and neuroimaging findings obtained using these games in healthy populations. We also address the factors that modulate behaviors in games and their neural bases. We then summarize the current findings obtained by using these games in depressed patients and discuss the clinical implications of these abnormal game behaviors. Finally, we briefly discuss future prospects that may further elucidate the clinical use of a game theory paradigm in MDD. PMID:26441689
Classical and quantum contents of solvable game theory on Hilbert space
International Nuclear Information System (INIS)
Cheon, Taksu; Tsutsui, Izumi
2006-01-01
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation
Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory
Yushkevich, A
1992-01-01
This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...
Lina Wu; Wenyi Lu; Ye Li
2016-01-01
Regarding heavy video game players for boys and super online chat lovers for girls as a symbolic phrase in the current adolescent culture, this project of data analysis verifies the displacement effect on deteriorating mathematics performance. To evaluate correlation or regression coefficients between a factor of playing video games or chatting online and mathematics performance compared with other factors, we use multivariate analysis technique and take gender difference into account. We fin...
Combinatorial neural codes from a mathematical coding theory perspective.
Curto, Carina; Itskov, Vladimir; Morrison, Katherine; Roth, Zachary; Walker, Judy L
2013-07-01
Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.
Teaching and Learning of Knot Theory in School Mathematics
Kawauchi, Akio
2012-01-01
This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives. Readers will find an extremely clear and concise introduction to the fundamentals of knot theory, an overview of curricular developments in Japan, and in particular a series of teaching
Turgut, Sedat; Temur, Özlem Dogan
2017-01-01
In this research, the effects of using game in mathematics teaching process on academic achievement in Turkey were examined by metaanalysis method. For this purpose, the average effect size value and the average effect size values of the moderator variables (education level, the field of education, game type, implementation period and sample size)…
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Mathematical tools for data mining set theory, partial orders, combinatorics
Simovici, Dan A
2014-01-01
Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the firs
Applying Game Theory in 802.11 Wireless Networks
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Tomas Cuzanauskas
2015-07-01
Full Text Available IEEE 802.11 is one of the most popular wireless technologies in recent days. Due to easiness of adaption and relatively low cost the demand for IEEE 802.11 devices is increasing exponentially. IEEE works in two bands 2.4 GHz and 5 GHz, these bands are known as ISM band. The unlicensed bands are managed by authority which set simple rules to follow when using unlicensed bands, the rules includes requirements as maximum power, out-of-band emissions control as well as interference mitigation. However these rules became outdated as IEEE 802.11 technology is emerging and evolving in hours the rules aren’t well suited for current capabilities of IEEE 802.11 devices. In this article we present game theory based algorithm for IEEE 802.11 wireless devices, we will show that by using game theory it’s possible to achieve better usage of unlicensed spectrum as well as partially decline CSMA/CA. Finally by using this approach we might relax the currently applied maximum power rules for ISM bands, which enable IEEE 802.11 to work on longer distance and have better propagation characteristics.
Games microbes play: The game theory behind cooperative sucrose metabolism in yeast
Gore, Jeff
2010-03-01
The origin of cooperation is a central challenge to our understanding of evolution. Microbial interactions can be manipulated in ways that animal interactions cannot, thus leading to growing interest in microbial models of cooperation and competition. In order for the budding yeast S. cerevisiae to grow on sucrose, the disaccharide must first be hydrolyzed by the enzyme invertase. This hydrolysis reaction is performed outside of the cytoplasm in the periplasmic space between the plasma membrane and the cell wall. Here we demonstrate that the vast majority (˜99%) of the monosaccharides created by sucrose hydrolysis diffuse away before they can be imported into the cell, thus making invertase production and secretion a cooperative behavior [1]. A mutant cheater strain that does not produce invertase is able to take advantage of and invade a population of wildtype cooperator cells. However, over a wide range of conditions, the wildtype cooperator can also invade a population of cheater cells. Therefore, we observe coexistence between the two strains in well-mixed culture at steady state resulting from the fact that rare strategies outperform common strategies---the defining features of what game theorists call the snowdrift game. A simple model of the cooperative interaction incorporating nonlinear benefits explains the origin of this coexistence. Glucose repression of invertase expression in wildtype cells produces a strategy which is optimal for the snowdrift game---wildtype cells cooperate only when competing against cheater cells. In disagreement with recent theory [2], we find that spatial structure always aids the evolution of cooperation in our experimental snowdrift game. [4pt] [1] Gore, J., Youk, H. & van Oudenaarden, A., Nature 459, 253 -- 256 (2009) [0pt] [2] Hauert, C. & Doebeli, M., Nature 428, 643 -- 646 (2004)
Cooperative games and network structures
Musegaas, Marieke
2017-01-01
This thesis covers various research topics involving cooperative game theory, a mathematical tool to analyze the cooperative behavior within a group of players. The focus is mainly on interrelations between operations research and cooperative game theory by analyzing specific types of cooperative
Setiawan, R.
2018-03-01
In this paper, Economic Order Quantity (EOQ) of probabilistic two-level supply – chain system for items with imperfect quality has been analyzed under service level constraint. A firm applies an active service level constraint to avoid unpredictable shortage terms in the objective function. Mathematical analysis of optimal result is delivered using two equilibrium scheme concept in game theory approach. Stackelberg’s equilibrium for cooperative strategy and Stackelberg’s Equilibrium for noncooperative strategy. This is a new approach to game theory result in inventory system whether service level constraint is applied by a firm in his moves.
Game theory at work: OR models and algorythms to solve multi-actor heterogeneous decision problems
Sáiz Pérez, M.E.
2007-01-01
Key words: Game theory, operations research, optimisation methods, algorithms. The objective of this thesis is to explore the potential of combining Game Theory (GT) models with Operations Research (OR) modelling. This includes development of algorithms to solve these complex OR models for
Using Game Theory and the Bible to Build Critical Thinking Skills
McCannon, Bryan C.
2007-01-01
The author describes a course designed to build the critical thinking skills of undergraduate economics students. The course introduces and uses game theory to study the Bible. Students gain experience using game theory to formalize events and, by drawing parallels between the Bible and common economic concepts, illustrate the pervasiveness of…
Williams, Miriam F.
2012-01-01
The author uses game theoretical models to identify technical communication breakdowns encountered during the notoriously confusing Texas Two-Step voting and caucusing process. Specifically, the author uses narrative theory and game theory to highlight areas where caucus participants needed instructions to better understand the rules of the game…
Mathematical analogies in physics. Thin-layer wave theory
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José M. Carcione
2014-03-01
Full Text Available Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law. In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect. The analogy is mainly illustrated with geophysical examples of propagation of S (shear, P (compressional, TM (transverse-magnetic and TE (transverse-electric waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.
Mathematical theory of Feynman path integrals an introduction
Albeverio, Sergio A; Mazzucchi, Sonia
2008-01-01
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-11-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-09-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
Change Of Learning Environment Using Game Production Theory, Methods And Practice
DEFF Research Database (Denmark)
Reng, Lars; Kofoed, Lise; Schoenau-Fog, Henrik
2018-01-01
will focus on cases in which development of games did change the learning environments into production units where students or employees were producing games as part of the learning process. The cases indicate that the motivation as well as the learning curve became very high. The pedagogical theories......Game Based Learning has proven to have many possibilities for supporting better learning outcomes, when using educational or commercial games in the classroom. However, there is also a great potential in using game development as a motivator in other kinds of learning scenarios. This study...... and methods are based on Problem Based Learning (PBL), but are developed further by combining PBL with a production-oriented/design based approach. We illustrate the potential of using game production as a learning environment with investigation of three game productions. We can conclude that using game...
The ecology of cancer from an evolutionary game theory perspective.
Pacheco, Jorge M; Santos, Francisco C; Dingli, David
2014-08-06
The accumulation of somatic mutations, to which the cellular genome is permanently exposed, often leads to cancer. Analysis of any tumour shows that, besides the malignant cells, one finds other 'supporting' cells such as fibroblasts, immune cells of various types and even blood vessels. Together, these cells generate the microenvironment that enables the malignant cell population to grow and ultimately lead to disease. Therefore, understanding the dynamics of tumour growth and response to therapy is incomplete unless the interactions between the malignant cells and normal cells are investigated in the environment in which they take place. The complex interactions between cells in such an ecosystem result from the exchange of information in the form of cytokines- and adhesion-dependent interactions. Such processes impose costs and benefits to the participating cells that may be conveniently recast in the form of a game pay-off matrix. As a result, tumour progression and dynamics can be described in terms of evolutionary game theory (EGT), which provides a convenient framework in which to capture the frequency-dependent nature of ecosystem dynamics. Here, we provide a tutorial review of the central aspects of EGT, establishing a relation with the problem of cancer. Along the way, we also digress on fitness and of ways to compute it. Subsequently, we show how EGT can be applied to the study of the various manifestations and dynamics of multiple myeloma bone disease and its preceding condition known as monoclonal gammopathy of undetermined significance. We translate the complex biochemical signals into costs and benefits of different cell types, thus defining a game pay-off matrix. Then we use the well-known properties of the EGT equations to reduce the number of core parameters that characterize disease evolution. Finally, we provide an interpretation of these core parameters in terms of what their function is in the ecosystem we are describing and generate
d=4 N=2 Field Theory And Physical Mathematics
CERN. Geneva
2017-01-01
I will explain the meaning of the two phrases in the title. Much of the talk will be a review of the renowned Seiberg-Witten formulation of the low-energy physics of certain four dimensional supersymmetric interacting quantum field theories. In the latter part of the talk I will briefly describe some of the significant progress that has been made in solving for the so-called BPS sector of the Hilbert space of these theories. Investigations into these physical questions have had a nontrivial impact on mathematics.
An introduction to the mathematical theory of finite elements
Oden, J T
2011-01-01
This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and co
Homotopy theory the mathematical works of J. H. C. whitehead
James, I M
1962-01-01
Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes.This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are
International Nuclear Information System (INIS)
Nwulu, Nnamdi I.; Xia, Xiaohua
2015-01-01
Highlights: • In this work, a game theory based DR program is integrated into the DEED problem. • Objectives are to minimize fuel and emissions costs and maximize the DR benefit. • Optimal generator output, customer load and customer incentive are determined. • Developed model is tested with two different scenarios. • Model provides superior results than independent optimization of DR or DEED. - Abstract: The dynamic economic emission dispatch (DEED) of electric power generation is a multi-objective mathematical optimization problem with two objective functions. The first objective is to minimize all the fuel costs of the generators in the power system, whilst the second objective seeks to minimize the emissions cost. Both objective functions are subject to constraints such as load demand constraint, ramp rate constraint, amongst other constraints. In this work, we integrate a game theory based demand response program into the DEED problem. The game theory based demand response program determines the optimal hourly incentive to be offered to customers who sign up for load curtailment. The game theory model has in built mechanisms to ensure that the incentive offered the customers is greater than the cost of interruption while simultaneously being beneficial to the utility. The combined DEED and game theoretic demand response model presented in this work, minimizes fuel and emissions costs and simultaneously determines the optimal incentive and load curtailment customers have to perform for maximal power system relief. The developed model is tested on two test systems with industrial customers and obtained results indicate the practical benefits of the proposed model
System of marketing deciding support based on game theory
Directory of Open Access Journals (Sweden)
Gordana Dukić
2008-12-01
Full Text Available Quantitative methods and models can be applied in numerous spheres of marketing deciding. The choice of optimal strategy in product advertising is one of the problems that the marketing-management often meets. The use of models developed within the framework of game theory makes significantly easier to find out the solutions of conflict situations that appear herewith. The system of deciding support presented in this work is based on the supposition that two opposed sides take part in the game. With the aim of deciding process promotion, the starting model incorporates computer simulation of percentile changes in the market share that represent elements of payment matrix. The supposition is that the random variables that represent them follow the normal division. It is necessary to carry out the evaluation of their parameters because of relevant data. Information techniques, computer and the adequate program applications take the special position in solving and analysis of the suggested model. This kind of their application represents the basic characteristic of the deciding support system.
An educational video game for nutrition of young people: Theory and design.
Ledoux, Tracey; Griffith, Melissa; Thompson, Debbe; Nguyen, Nga; Watson, Kathy; Baranowski, Janice; Buday, Richard; Abdelsamad, Dina; Baranowski, Tom
2016-08-01
Playing Escape from DIAB (DIAB) and Nanoswarm (NANO) , epic video game adventures, increased fruit and vegetable consumption among a multi-ethnic sample of 10-12 year old children during pilot testing. Key elements of both games were educational mini-games embedded in the overall game that promoted knowledge acquisition regarding diet, physical activity and energy balance. 95-100% of participants demonstrated mastery of these mini-games suggesting knowledge acquisition. This article describes the process of designing and developing the educational mini-games. A secondary purpose was to explore the experience of children while playing the games. The educational games were based on Social Cognitive and Mastery Learning Theories. A multidisciplinary team of behavioral nutrition, PA, and video game experts designed, developed, and tested the mini-games. Alpha testing revealed children generally liked the mini-games and found them to be reasonably challenging. Process evaluation data from pilot testing revealed almost all participants completed nearly all educational mini-games in a reasonable amount of time suggesting feasibility of this approach. Future research should continue to explore the use of video games in educating children to achieve healthy behavior changes.
An educational video game for nutrition of young people: Theory and design
Ledoux, Tracey; Griffith, Melissa; Thompson, Debbe; Nguyen, Nga; Watson, Kathy; Baranowski, Janice; Buday, Richard; Abdelsamad, Dina; Baranowski, Tom
2016-01-01
Background Playing Escape from DIAB (DIAB) and Nanoswarm (NANO), epic video game adventures, increased fruit and vegetable consumption among a multi-ethnic sample of 10–12 year old children during pilot testing. Key elements of both games were educational mini-games embedded in the overall game that promoted knowledge acquisition regarding diet, physical activity and energy balance. 95–100% of participants demonstrated mastery of these mini-games suggesting knowledge acquisition. Aim This article describes the process of designing and developing the educational mini-games. A secondary purpose was to explore the experience of children while playing the games. Method The educational games were based on Social Cognitive and Mastery Learning Theories. A multidisciplinary team of behavioral nutrition, PA, and video game experts designed, developed, and tested the mini-games. Results Alpha testing revealed children generally liked the mini-games and found them to be reasonably challenging. Process evaluation data from pilot testing revealed almost all participants completed nearly all educational mini-games in a reasonable amount of time suggesting feasibility of this approach. Conclusions Future research should continue to explore the use of video games in educating children to achieve healthy behavior changes. PMID:27547019
Abdul Hadi, Normi; Mohd Noor, Norlenda; Abd Halim, Suhaila; Alwadood, Zuraida; Khairol Azmi, Nurul Nisa'
2013-04-01
Mathematics is a basic subject in primary and secondary schools. Early exposure to mathematics is very important since it will affect the student perception towards this subject for their entire life. Therefore, a program called 'Mini Hari Matematik' was conducted to expose the basic mathematics concept through some games which fit the knowledge of Standard four and five students. A questionnaire regarding student perception towards this subject was distributed before and after the program. From the analysis, the program has positively changed the student's perception towards mathematics.
The Bus Station Spacing Optimization Based on Game Theory
Directory of Open Access Journals (Sweden)
Changjiang Zheng
2015-01-01
Full Text Available With the development of city, the problem of traffic is becoming more and more serious. Developing public transportation has become the key to solving this problem in all countries. Based on the existing public transit network, how to improve the bus operation efficiency, and reduce the residents transit trip cost has become a simple and effective way to develop the public transportation. Bus stop spacing is an important factor affecting passengers’ travel time. How to set up bus stop spacing has become the key to reducing passengers’ travel time. According to comprehensive traffic survey, theoretical analysis, and summary of urban public transport characteristics, this paper analyzes the impact of bus stop spacing on passenger in-bus time cost and out-bus time cost and establishes in-bus time and out-bus time model. Finally, the paper gets the balance best station spacing by introducing the game theory.
A short review of game theory for neurosurgeons.
Steiger, H-J; Steiger, U R
2011-02-01
Neurosurgery and medicine in general are increasingly dominated by economic factors and considerations. Physicians themselves have partially adopted economic terminology, although they rarely have a profound knowledge of economics. Today game theory is one of the most important factors driving microeconomics, which is the competition for limited resources within a small group of individuals. The purpose of this article is to give a short introduction to game theory and its application to the healthcare system. The Prisoner's Dilemma considers strategies between two persons. In the classic version two burglars are caught. Each could confess and be released from jail if the other does not confess--who will then get a long term in prison. If both confess, both get an intermediate time in jail, and if no one confesses, both get a mild sentence. Wanting to be released from jail, they both confess and get the intermediate term in prison. This remarkable result, initially described by John von Neumann in 1928 and showing that individually rational actions can result in both persons becoming worse off, had a great impact on modern social science. Other scenarios are more complex. The Nash Equilibrium is a wider concept. If there is a set of strategies with the property that no player can benefit by changing his strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium. Another concept particularly important in sociology is the Pareto criterion. If no one can be made better off without making somebody else worse off, then that outcome is Pareto optimal. Respecting these basic principles is a necessary precondition for successful deals and cooperative projects. © Georg Thieme Verlag KG Stuttgart · New York.
Bohmian mechanics. The physics and mathematics of quantum theory
International Nuclear Information System (INIS)
Duerr, Detlef; Teufel, Stefan
2009-01-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Bohmian mechanics. The physics and mathematics of quantum theory
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.
2009-07-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Analysis of safety supervision effect on coal mine using game theory
Energy Technology Data Exchange (ETDEWEB)
Zhou Min; Xiao Zhong-hai [China University of Mining & Technology, Xuzhou (China). School of Management
2006-07-01
A two-phase game model was constructed based on economic game theory to improve the inefficient supervision conditions of coalmining enterprises' safety production. The inner mechanism of safety supervision system was carefully studied. The strategy set of the dynamic game-theory relations between colliery proprietor and safety supervision department and the strict competitive game-theory relations between safety supervision department and workers at the production line was analyzed. The conditions of achieving the dominant-strategy equilibrium were revealed. Upon this basis, the possible solution set of safety benefit distribution for the cooperative game-theory of triple party was obtained and the effective and cooperative fair solution was formed. Finally, conclusions are drawn as follows: the combination of necessary penalty to supervisors and operators with the fair distribution of safety benefits can realize the zero-defect of operational violation, so that the violation behavior can be completely avoided. 10 refs., 7 figs.
Campos, Helena; Moreira, Rute
2016-04-01
This article is based on an experiment using the game 'Caminhando e Calculando' (Moving and Calculating) in order to analyse the potential of the game as an educational resource for the teaching and learning of mathematics in Portuguese middle schools, where most students are 10 or 11 years old. Students' data obtained during the games will be used to analyse the different options used for solving the game, identifying its potential and its weaknesses. We start with a theoretical analysis of games as an inherent element of human culture. Combining our innate desire for fun with the different types of teaching and learning styles allows for fun and knowledge to be combined into more efficient and meaningful types of knowledge. Playing games are a primordial aspect of what it means to be a child and they develop within a motivating environment; therefore, not to take advantage of games as a learning resource would be to neglect an important asset. With regard to mathematics, emphasis will be given to the advantages that this teaching and learning tool provides for certain mathematical processes, such as problem-solving.
Hsu, Fei-Man; Chen, Pao-Yang
2017-03-01
Von Neumann and Morgenstern published the Theory of Games and Economic Behavior in 1944, describing game theory as a model in which intelligent rational decision-makers manage to find their best strategies in conflict, cooperative or other mutualistic relationships to acquire the greatest benefit [1]. This model was subsequently incorporated in ecology to simulate the ;fitness; of a species during natural selection, designated evolutionary game theory (EGT) [2]. Wang et al. proposed ;epiGame;, taking paternal and maternal genomes as ;intelligent; players that compete, cooperate or both during embryogenesis to maximize the fitness of the embryo [3]. They further extended game theory to an individual or single cell environment. During early zygote development, DNA methylation is reprogrammed such that the paternal genome is demethylated before the maternal genome. After the reset, the blastocyst is re-methylated during embryogenesis. At that time, the paternal and maternal genomes have a conflict of interest related to the expression of their own genes. The proposed epiGame models such interactive regulation between the parental genomes to reach a balance for embryo development (equation (2)).
Investigating the Learning-Theory Foundations of Game-Based Learning: A Meta-Analysis
Wu, W-H.; Hsiao, H-C.; Wu, P-L.; Lin, C-H.; Huang, S-H.
2012-01-01
Past studies on the issue of learning-theory foundations in game-based learning stressed the importance of establishing learning-theory foundation and provided an exploratory examination of established learning theories. However, we found research seldom addressed the development of the use or failure to use learning-theory foundations and…
Behavioural studies of strategic thinking in games.
Camerer, Colin F.
2003-05-01
Game theory is a mathematical language for describing strategic interactions, in which each player's choice affects the payoff of other players (where players can be genes, people, companies, nation-states, etc.). The impact of game theory in psychology has been limited by the lack of cognitive mechanisms underlying game-theoretic predictions. 'Behavioural game theory' is a recent approach linking game theory to cognitive science by adding cognitive details about 'social utility functions', theories of limits on iterated thinking, and statistical theories of how players learn and influence others. New directions include the effects of game descriptions on choice ('framing'), strategic heuristics, and mental representation. These ideas will help root game theory more deeply in cognitive science and extend the scope of both enterprises.
Game theory: Parts I and II - with 88 solved exercises. An open access textbook
Bonanno, Giacomo
2015-01-01
This is a draft of the first half of an open access textbook on game theory. I hope to complete the entire book by the end of 2015. After teaching game theory (at both the undergraduate and graduate level) at the University of California, Davis for 25 years, I decided to organize all my teaching material in a textbook. There are many excellent textbooks in game theory and there is hardly any need for a new one. However, there are two distinguishing features of this textbook: (1) it is open ac...
Applications of multi-criteria and game theory approaches manufacturing and logistics
Hennet, Jean-Claude; Tiwari, Manoj
2014-01-01
Aligning the latest practices, innovations and case studies with academic frameworks and theories, the broad area of multi-criteria and game theory applications in manufacturing and logistics is covered in comprehensive details. Part 1 presents ‘multi-criteria applications’ and includes chapters on logistics with a focus on vehicle routing problems, a multi-objective decision making approach to select the best storage policy and an exploratory study to predict the most important factors that can lead to successful mobile supply chain management adoption for manufacturing firms. Part 2 covers ‘game theory applications’ and encompasses the process of forming a coalition within a corporate network to the problem of integrating inventory and distribution optimization together with game theory to effectively manage supply networks. Providing a forum to investigate, exchange novel ideas and disseminate knowledge covering the broad area of multi-criteria and game theory applications in manufacturing and l...
Directory of Open Access Journals (Sweden)
Mahesa Jenar
2015-06-01
a mathematical approach that can analyze the decision-making process that involves two or more interests. In this study game theory will be used to analyze the decisions of relevant interests. The result shows that the model of game theory can describe the relationship between producer and consumer transactions in the buffer stock scheme. Moreover, game theory can describe some of the conditions in the buffer stock scheme through a strategy developed.
Non-cooperative stochastic differential game theory of generalized Markov jump linear systems
Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning
2017-01-01
This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...
Masters of Theory Cambridge and the Rise of Mathematical Physics
Warwick, Andrew
2011-01-01
Winner of the the Susan Elizabeth Abrams Prize in History of Science.When Isaac Newton published the Principia three centuries ago, only a few scholars were capable of understanding his conceptually demanding work. Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these "masters of theory" led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cam
Directory of Open Access Journals (Sweden)
Blaženka Divjak
2011-06-01
Full Text Available Normal 0 21 false false false SH X-NONE X-NONE Information technologies are an integral part of a contemporary society which bases its progress on knowledge being one goal of education. Beside acquiring knowledge, skills and routines, the goal of education is to create a complete individual who can rationally and timely make decisions, purposefully react in new situations and be trained for life-long learning. In order to accomplish all this, it is necessary to make educational process more creative, contemporary and adjusted to new generations of computer literate pupils who demand quicker and more frequent interactions, a lot of information at the same time, generations who quickly acquire rules of computer games. Computer games meeting pedagogical criteria should become an integral part of learning. Teaching with mathematical computer games, which fulfil pedagogical criteria, influences pupils’ motivation, learning, retention and forgetting. This paper provides a review of literature in this field and determines whether the use of mathematical computer games contributes to more efficient realisation of educational goals at all level of education. Furthermore, considering prior research we have attempted to establish whether the use of mathematical games for teaching has an impact on the formation of a positive attitude of pupils of different ages toward the subject of mathematics, their motivation and knowledge acquisition when compared to learning without computer games. Finally, we have analysed different research methods concerning this issue and assessed the impact of pedagogically designed mathematical computer games on the realisation of educational goals and quality improvement of teaching and learning.
Wang, Yaqun
2017-03-01
The authors are to be congratulated for a thought-provoking article [1], which reviews the epigenetic game theory (epiGame) that utilizes differential equations to study the epigenetic control of embryo development. It is a novel application of evolutionary game theory and provides biology researchers with useful methodologies to address scientific questions related to biological coordination of competition and cooperation.
Simulating Serious Games: A Discrete-Time Computational Model Based on Cognitive Flow Theory
Westera, Wim
2018-01-01
This paper presents a computational model for simulating how people learn from serious games. While avoiding the combinatorial explosion of a games micro-states, the model offers a meso-level pathfinding approach, which is guided by cognitive flow theory and various concepts from learning sciences. It extends a basic, existing model by exposing…
Game as a Career Metaphor: A Chaos Theory Career Counselling Application
Pryor, Robert George Leslie; Bright, Jim E. H.
2009-01-01
The potential of game as a career metaphor for use in counselling is explored and it is argued that it has been largely overlooked in the literature to date. This metaphor is then explicitly linked with the Chaos Theory of Careers (CTC), by showing how the notion of attractors within the CTC can be illustrated effectively using games metaphors.…
Zheng, Xiu-Deng; Tao, Yi
2017-03-01
The evolutionary significance of the interaction between paternal and maternal genomes in fertilized zygotes is a very interesting and challenging question. Wang et al. developed the concept of epigenetic game theory, and they try to use this concept to explain the interaction between paternal and maternal genomes in fertilized zygotes [1]. They emphasize that the embryogenesis can be considered as an ecological system in which two highly distinct and specialized gametes coordinate through either cooperation or competition, or both, to maximize the fitness of embryos under Darwinian selection. More specifically, they integrate game theory to model the pattern of coordination of paternal genome and maternal genomes mediated by DNA methylation dynamics, and they called this epigenetic game theory.
Haagsma, M.C.; King, D.L.; Pieterse, M.E.; Peters, O.
2013-01-01
Although excessive video gaming has been linked to a range of psychological problems in young people, there have been few systematic attempts to conceptualize problem gaming using established psychological theory. The aim of this study was to examine problematic game use (PGU) using the Theory of
Haagsma, Maria C.; King, Daniel L.; Pieterse, Marcel E.; Peters, Oscar
2013-01-01
Although excessive video gaming has been linked to a range of psychological problems in young people, there have been few systematic attempts to conceptualize problem gaming using established psychological theory. The aim of this study was to examine problematic game use (PGU) using the Theory of Planned Behavior (TPB). A two-wave, six-month…
Haagsma, M.C.; King, Daniel L.; Pieterse, Marcel E.; Peters, O.
2013-01-01
Although excessive video gaming has been linked to a range of psychological problems in young people, there have been few systematic attempts to conceptualize problem gaming using established psychological theory. The aim of this study was to examine problematic game use (PGU) using the Theory of
Oriented matroid theory as a mathematical framework for M-theory
Nieto, J. A.
2006-01-01
We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over $M$-theory. As a consequence of our analysis we find a new type of action for extended systems which combines dually the $p$-brane and its dual $p^{\\perp}$-brane.
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina
2013-06-01
In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."
Wan, Chin-Sheng; Chiou, Wen-Bin
2006-06-01
Obviously, the negative impact of online games has received much attention as well as having become a popular research topic. This research explored, from flow theory and humanistic needs theory, the psychological motivations of Taiwanese adolescents who are addicted to online games. The purpose of Study 1 was to investigate the relationship between players' flow state and their online games addiction. The results indicated that flow state was negatively correlated with addictive inclination and it was not a significant predictor for players' subsequent additive inclination. Findings also revealed that the addicts' flow state was significantly lower than the nonaddicts. Thus, flow state might not be the key psychological mechanism of players' addiction. In Study 2, the results showed that the psychological needs of players of online games were close to the two-factor theory which depicts satisfaction and dissatisfaction dimensions. Addicted players' need-gratification was similar to the feature of dissatisfactory factor. That is, the absence of playing online games is more likely to generate sense of dissatisfaction; the addicts' compulsive use of online games seems to stem from the relief of dissatisfaction rather than the pursuit of satisfaction. In contrast, online games tend to provide the nonaddicts with a sense of satisfaction rather than a sense of dissatisfaction.
Sie, Rory
2012-01-01
Sie, R. L. L. (2012). COalitions in COOperation Networks (COCOON): Social Network Analysis and Game Theory to Enhance Cooperation Networks (Unpublished doctoral dissertation). September, 28, 2012, Open Universiteit in the Netherlands (CELSTEC), Heerlen, The Netherlands.
a review of game theory approach to cyber security risk management
African Journals Online (AJOL)
HOD
Keywords: Cyber Security, Risk Management, Game Theory, Model. 1. INTRODUCTION. Risk is ... behaviors. This implies they are triggered by self- motivated goal .... embrace diligence verification of the recipient of the email as well as lack of ...
Anttila, Jani; Annila, Arto
2011-10-01
A course of a game is formulated as a physical process that will consume free energy in the least time. Accordingly, the rate of entropy increase is the payoff function that will subsume all forms of free energy that motivate diverse decisions. Also other concepts of game theory are related to their profound physical counterparts. When the physical portrayal of behavior is mathematically analyzed, the course of a game is found to be inherently unpredictable because each move affects motives in the future. Despite the non-holonomic character of the natural process, the objective of consuming free energy in the least time will direct an extensive-form game toward a Lyapunov-stable point that satisfies the minimax theorem.
Inductive game theory and the dynamics of animal conflict.
Directory of Open Access Journals (Sweden)
Simon DeDeo
2010-05-01
Full Text Available Conflict destabilizes social interactions and impedes cooperation at multiple scales of biological organization. Of fundamental interest are the causes of turbulent periods of conflict. We analyze conflict dynamics in an monkey society model system. We develop a technique, Inductive Game Theory, to extract directly from time-series data the decision-making strategies used by individuals and groups. This technique uses Monte Carlo simulation to test alternative causal models of conflict dynamics. We find individuals base their decision to fight on memory of social factors, not on short timescale ecological resource competition. Furthermore, the social assessments on which these decisions are based are triadic (self in relation to another pair of individuals, not pairwise. We show that this triadic decision making causes long conflict cascades and that there is a high population cost of the large fights associated with these cascades. These results suggest that individual agency has been over-emphasized in the social evolution of complex aggregates, and that pair-wise formalisms are inadequate. An appreciation of the empirical foundations of the collective dynamics of conflict is a crucial step towards its effective management.
Esmaeili, Maryam; Bahrini, Aram; Shayanrad, Sepideh
2015-12-01
Oil and gas as the non-renewable resources are considered very valuable for the countries with petroleum economics. These resources are not only diffused equally around the world, but also they are common in some places which their neighbors often come into conflicts. Consequently, it is vital for those countries to manage their resource utilization. Lately, game theory was applied in conflict resolution of common resources, such as water, which is a proof of its efficacy and capability. This paper models the conflicts between Iran and its neighbors namely Qatar and Iraq between their oil and gas common resources using game theory approach. In other words, the future of these countries will be introduced and analyzed by some well-known 2 × 2 games to achieve a better perspective of their conflicts. Because of information inadequacy of the players, in addition to Nash Stability, various solution concepts are used based on the foresight, disimprovements, and knowledge of preferences. The results of mathematical models show how the countries could take a reasonable strategy to exploit their common resources.
Plant extractivism in light of game theory: a case study in northeastern Brazil
Silva, Rafael RV; Gomes, Laura Jane; Albuquerque, Ulysses Paulino
2015-01-01
Background Game theory enables the predictive study of the behavior of agents that recognize the mutual interdependence of their decisions and act rationally and strategically to maximize their own gains. In this paper, the extractivism of pequi (Caryocar coriaceum Wittm.) and fava d?anta (Dimorphandra gardneriana Tul.) in an area of common use of the semiarid region of northeastern Brazil is described as a model to illustrate a practical application of game theory in the interpretation of th...
A cooperative game theory approach to transmission planning in power systems
Contreras, Javier
The rapid restructuring of the electric power industry from a vertically integrated entity into a decentralized industry has given rise to complex problems. In particular, the transmission component of the electric power system requires new methodologies to fully capture this emerging competitive industry. Game theory models are used to model strategic interactions in a competitive environment. This thesis presents a new decentralized framework to study the transmission network expansion problem using cooperative game theory. First, the players and the rules of the game are defined. Second, a coalition formation scheme is developed. Finally, the optimized cost of expansion is allocated based on the history of the coalition formation.
Broadening the role of theory in mathematics education research
DEFF Research Database (Denmark)
Pais, Alexandre; Stentoft, Diana; Valero, Paola
2010-01-01
In C. Bergsten, E. Jablonka and T. Wedege (Eds), Mathematics and mathematics education: Cultural and social dimensions. Proceedings of MADIF7, The Seventh Mathematics Education Research Seminar, Stockholm, January 26-27, 2010. Linköping: SMDF....
Game Theory of Pollution: National Policies and Their International Effects
Schüller, Katharina; Stankova, Katerina; Thuijsman, Frank
2017-01-01
In this paper we put forward a simple game-theoretical model of pollution control, where each country is in control of its own pollution, while the environmental effects of policies do not stop at country borders. In our noncooperative differential game, countries as players minimize the present
Matrix analysis for associated consistency in cooperative game theory
Xu, G.; Driessen, Theo; Sun, H.; Sun, H.
Hamiache's recent axiomatization of the well-known Shapley value for TU games states that the Shapley value is the unique solution verifying the following three axioms: the inessential game property, continuity and associated consistency. Driessen extended Hamiache's axiomatization to the enlarged
Mathematical formalization of theories of motivation proposed by Maslow and Herzberg
Kotliarov,Ivan
2008-01-01
Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of sp...
Turkay, Selen; Hoffman, Daniel; Kinzer, Charles K.; Chantes, Pantiphar; Vicari, Christopher
2014-01-01
Researchers have argued that an effort should be made to raise teachers' and parents' awareness of the potentially positive educational benefits of playing video games (e.g., see Baek, 2008). One part of this effort should be to increase understanding of how video games can be situated within teachers' existing goals and knowledge…
Model of the extensive form game with the financial rewards
Erbsová, Markéta
2009-01-01
The aim of this Bachelor thesis is the analysis and presentation of the original extensive form game with the financial rewards, which is called Výměna (Exchange). In the theoretical part we will describe the basic concepts of Game Theory, especially the game in an explicit form. In the practical part we will deal with the game Výměna (Exchange) in itself. Determine the rules of the game, the graphic form of the game and formulate a mathematical model of the game. Individual parts of the game...
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
The combination of system dynamics and game theory in analyzing oligopoly markets
Directory of Open Access Journals (Sweden)
Ali Mohammadi
2016-04-01
Full Text Available In this paper, we present a hybrid method of game theory and dynamic systems to study the behavior of firms in an oligopoly market. The aim of this study is to build a model for an oligopoly game on the basis of feedback loops and system dynamics approach and to solve the resulted problems under some special conditions where traditional game theory methods are unable to handle. The method includes a combination of qualitative methods including interviews with industry experts to prepare the model and quantitative methods of system dynamics, simulation methodologies and game theory. The results indicate that competitive behavior and the important parameters such as volume of demand, interest rates and price fluctuation will be stabilized after a transition period.
Nejem, Khamis Mousa; Muhanna, Wafa
2013-01-01
The purpose of this study was to investigate the effect of using computer games in teaching mathematics on developing the number sense of fourth grade students. To achieve this purpose a study sample of (81) students was selected from the fourth grade. This sample was divided into two groups. One group was randomly chosen to be the experimental…
Kazak, Sibel; Pratt, Dave
2017-01-01
This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers' use of probability models for a chance game, where the sum of two dice matters in…
Bai, Haiyan; Pan, Wei; Hirumi, Astusi; Kebritchi, Mansureh
2012-01-01
This research study assessed the effectiveness of a three-dimensional mathematics game, DimensionM, through a pretest-posttest control group quasi-experimental design. Participants consisted of 437 eighth graders. The classrooms were randomly assigned either to the treatment group that utilized DimensionM as a supplement to regular classroom…
Frederick-Jonah, Toinpere Mercy; Igbojinwaekwu, Patrick Chukwuemeka
2015-01-01
This study investigated the effects of game and poem-enhanced instructional strategies on students' interest in mathematics. The moderating effects of verbal ability were also examined on the dependent variable. A quasi-experimental design was adopted. Three hundred and forty four students in the sixth year of their primary education (primary 6…
Fostering the Development of Logico-Mathematical Thinking in a Card Game at Ages 5-6
Kamii, Constance; Kato, Yasuhiko
2005-01-01
A class of 14 kindergartners in Japan was videotaped while playing a card game in groups of three involving the placement of cards in numerical order. The children were followed up in first grade, and it was found that development in one area of logico-mathematical knowledge (for example, the making of temporal relationships) stimulates…
Rough Set Theory Based Fuzzy TOPSIS on Serious Game Design Evaluation Framework
Directory of Open Access Journals (Sweden)
Chung-Ho Su
2013-01-01
Full Text Available This study presents a hybrid methodology for solving the serious game design evaluation in which evaluation criteria are based on meaningful learning, ARCS motivation, cognitive load, and flow theory (MACF by rough set theory (RST and experts’ selection. The purpose of this study tends to develop an evaluation model with RST based fuzzy Delphi-AHP-TOPSIS for MACF characteristics. Fuzzy Delphi method is utilized for selecting the evaluation criteria, Fuzzy AHP is used for analyzing the criteria structure and determining the evaluation weight of criteria, and Fuzzy TOPSIS is applied to determine the sequence of the evaluations. A real case is also used for evaluating the selection of MACF criteria design for four serious games, and both the practice and evaluation of the case could be explained. The results show that the playfulness (C24, skills (C22, attention (C11, and personalized (C35 are determined as the four most important criteria in the MACF selection process. And evaluation results of case study point out that Game 1 has the best score overall (Game 1 > Game 3 > Game 2 > Game 4. Finally, proposed evaluation framework tends to evaluate the effectiveness and the feasibility of the evaluation model and provide design criteria for relevant multimedia game design educators.
Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.
Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M
2016-06-01
The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.
Games unifying logic, language, and philosophy
Majer, Ondrej; Tulenheimo, Tero
2008-01-01
This unique volume presents mathematical game theory as an interface between logic and philosophy. It provides a discussion of various aspects of this interaction, covers new technical results and examines the philosophical insights that these have yielded.
Action being character: a promising perspective on the solution concept of game theory.
Deng, Kuiying; Chu, Tianguang
2011-05-09
The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations.
Understanding student use of mathematics in IPLS with the Math Epistemic Games Survey
Eichenlaub, Mark; Hemingway, Deborah; Redish, Edward F.
2017-01-01
We present the Math Epistemic Games Survey (MEGS), a new concept inventory on the use of mathematics in introductory physics for the life sciences. The survey asks questions that are often best-answered via techniques commonly-valued in physics instruction, including dimensional analysis, checking special or extreme cases, understanding scaling relationships, interpreting graphical representations, estimation, and mapping symbols onto physical meaning. MEGS questions are often rooted in quantitative biology. We present preliminary data on the validation and administration of the MEGS in a large, introductory physics for the life sciences course at the University of Maryland, as well as preliminary results on the clustering of questions and responses as a guide to student resource activation in problem solving. This material is based upon work supported by the US National Science Foundation under Award No. 15-04366.
International Nuclear Information System (INIS)
Anttila, Jani; Annila, Arto
2011-01-01
A course of a game is formulated as a physical process that will consume free energy in the least time. Accordingly, the rate of entropy increase is the payoff function that will subsume all forms of free energy that motivate diverse decisions. Also other concepts of game theory are related to their profound physical counterparts. When the physical portrayal of behavior is mathematically analyzed, the course of a game is found to be inherently unpredictable because each move affects motives in the future. Despite the non-holonomic character of the natural process, the objective of consuming free energy in the least time will direct an extensive-form game toward a Lyapunov-stable point that satisfies the minimax theorem. -- Highlights: → Behavior in the context of game theory is described as a natural process. → The rate of entropy increase, derived from statistical physics of open systems, is identified as the payoff function. → Entropy as the payoff function also clarifies motives of collaboration and subjective nature of decision making. → Evolutionary equation of motion that accounts for the course of a game is inherently unpredictable.
Is There an Optimal Strategic Oil Reserve for Each Country? A Study Based on the Game Theory
DEFF Research Database (Denmark)
Yang, Junan; Cong, Ronggang
2014-01-01
-cooperative game theory. It also analyzes the establishment of strategic oil reserve among different countries based on the coalition game theory and presents the core solution for it. The results show that based on a certain constraint mechanism, it is feasible for different countries to establish their own...... suitable strategic oil reserves in theory and practice....
Cryer, Patricia
1988-01-01
Develops models for participants' behaviors in games, simulations, and workshops based on Catastrophe Theory and Herzberg's two-factor theory of motivation. Examples are given of how these models can be used, both for describing and understanding the behaviors of individuals, and for eliciting insights into why participants behave as they do. (11…
Teaching Prospect Theory with the "Deal or No Deal" Game Show
Baker, Ardith; Bittner, Teresa; Makrigeorgis, Christos; Johnson, Gloria; Haefner, Joseph
2010-01-01
Recent evidence indicates that decision makers are more sensitive to potential losses than gains. Loss aversion psychology has led behavioural economists to look beyond expected utility by developing "prospect theory." We demonstrate this theory using the "Deal or No Deal" game show.
Game theory application to operation control and pricing in deregulated power systems
International Nuclear Information System (INIS)
Yokoyama, G.R.
2000-01-01
Rapid move to a market-based electric power industry will significantly change electric utility operations. In this paper, we consider economic load dispatching rules in power systems under competitive environment when independent power producers (IPPs) are introduced and analyze their economic consequences by using game theory. An electric utility and IPPs are included in the model as players of the game where IPPs enter into the game firstly as a group, and secondly as individually. The utility and IPPs intend to maximize their own profit. We mainly use the Stackelberg strategy game theory and Nash equilibrium solution to analyze the negotiation process between the electric utility and IPPS, since it is widely recognized as rational decisions for competitive markets in terms of axiom. (author)
Directory of Open Access Journals (Sweden)
Urszula Markowska-Przybyła
2014-01-01
Full Text Available Although studies using experimental game theory have been carried out in various countries, no such major study has occurred in Poland. The study described here aims to investigate generalized trust and reciprocation among Polish students. In the literature, these traits are seen to be positively correlated with economic growth. Poland is regarded as the most successful post-soviet bloc country in transforming to a market economy but the level of generalised trust compared to other postcommunist countries is reported to be low. This study aims to see to what degree this reported level of generalised trust is visible amongst young Poles via experimental game theory, along with a questionnaire. The three games to be played have been described. Bayesian equilibria illustrating behavior observed in previous studies have been derived for two of these games and the experimental procedure has been described. (original abstract
Nash, Jr, John Forbes
2016-01-01
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
Zhang, Yuan-Ming; Zhang, Yinghao; Guo, Mingyue
2017-03-01
Wang's et al. article [1] is the first to integrate game theory (especially evolutionary game theory) with epigenetic modification of zygotic genomes. They described and assessed a modeling framework based on evolutionary game theory to quantify, how sperms and oocytes interact through epigenetic processes, to determine embryo development. They also studied the internal mechanisms for normal embryo development: 1) evolutionary interactions between DNA methylation of the paternal and maternal genomes, and 2) the application of game theory to formulate and quantify how different genes compete or cooperate to regulate embryogenesis through methylation. Although it is not very comprehensive and profound regarding game theory modeling, this article bridges the gap between evolutionary game theory and the epigenetic control of embryo development by powerful ordinary differential equations (ODEs). The epiGame framework includes four aspects: 1) characterizing how epigenetic game theory works by the strategy matrix, in which the pattern and relative magnitude of the methylation effects on embryogenesis, are described by the cooperation and competition mechanisms, 2) quantifying the game that the direction and degree of P-M interactions over embryo development can be explained by the sign and magnitude of interaction parameters in model (2), 3) modeling epigenetic interactions within the morula, especially for two coupled nonlinear ODEs, with explicit functions in model (4), which provide a good fit to the observed data for the two sexes (adjusted R2 = 0.956), and 4) revealing multifactorial interactions in embryogenesis from the coupled ODEs in model (2) to triplet ODEs in model (6). Clearly, this article extends game theory from evolutionary game theory to epigenetic game theory.
DEFF Research Database (Denmark)
Putra, Zetra Hainul; Witri, Gustimal
2017-01-01
Théorie Anthropologique du Didactique/Anthropological Theory of the Didactic (ATD) is a new theory on didactic mathematics that was introduced by a French mathematician, Chevellard, in 1991. The ATD is an epistemological model of mathematical knowledge that can be applied to investigate human mat...
Mathematics Education as a Proving-Ground for Information-Processing Theories.
Greer, Brian, Ed.; Verschaffel, Lieven, Ed.
1990-01-01
Five papers discuss the current and potential contributions of information-processing theory to our understanding of mathematical thinking as those contributions affect the practice of mathematics education. It is concluded that information-processing theories need to be supplemented in various ways to more adequately reflect the complexity of…
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…
Mathematical finance theory review and exercises from binomial model to risk measures
Gianin, Emanuela Rosazza
2013-01-01
The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.
Health Behavior Theory in Physical Activity Game Apps: A Content Analysis
Moxley, Victor BA; MacDonald, Elizabeth
2015-01-01
Background Physical activity games developed for a mobile phone platform are becoming increasingly popular, yet little is known about their content or inclusion of health behavior theory (HBT). Objective The objective of our study was to quantify elements of HBT in physical activity games developed for mobile phones and to assess the relationship between theoretical constructs and various app features. Methods We conducted an analysis of exercise and physical activity game apps in the Apple App Store in the fall of 2014. A total of 52 apps were identified and rated for inclusion of health behavior theoretical constructs using an established theory-based rubric. Each app was coded for 100 theoretical items, containing 5 questions for 20 different constructs. Possible total theory scores ranged from 0 to 100. Descriptive statistics and Spearman correlations were used to describe the HBT score and association with selected app features, respectively. Results The average HBT score in the sample was 14.98 out of 100. One outlier, SuperBetter, scored higher than the other apps with a score of 76. Goal setting, self-monitoring, and self-reward were the most-reported constructs found in the sample. There was no association between either app price and theory score (P=.5074), or number of gamification elements and theory score (P=.5010). However, Superbetter, with the highest HBT score, was also the most expensive app. Conclusions There are few content analyses of serious games for health, but a comparison between these findings and previous content analyses of non-game health apps indicates that physical activity mobile phone games demonstrate higher levels of behavior theory. The most common theoretical constructs found in this sample are known to be efficacious elements in physical activity interventions. It is unclear, however, whether app designers consciously design physical activity mobile phone games with specific constructs in mind; it may be that games lend
Health Behavior Theory in Physical Activity Game Apps: A Content Analysis.
Payne, Hannah E; Moxley, Victor Ba; MacDonald, Elizabeth
2015-07-13
Physical activity games developed for a mobile phone platform are becoming increasingly popular, yet little is known about their content or inclusion of health behavior theory (HBT). The objective of our study was to quantify elements of HBT in physical activity games developed for mobile phones and to assess the relationship between theoretical constructs and various app features. We conducted an analysis of exercise and physical activity game apps in the Apple App Store in the fall of 2014. A total of 52 apps were identified and rated for inclusion of health behavior theoretical constructs using an established theory-based rubric. Each app was coded for 100 theoretical items, containing 5 questions for 20 different constructs. Possible total theory scores ranged from 0 to 100. Descriptive statistics and Spearman correlations were used to describe the HBT score and association with selected app features, respectively. The average HBT score in the sample was 14.98 out of 100. One outlier, SuperBetter, scored higher than the other apps with a score of 76. Goal setting, self-monitoring, and self-reward were the most-reported constructs found in the sample. There was no association between either app price and theory score (P=.5074), or number of gamification elements and theory score (P=.5010). However, Superbetter, with the highest HBT score, was also the most expensive app. There are few content analyses of serious games for health, but a comparison between these findings and previous content analyses of non-game health apps indicates that physical activity mobile phone games demonstrate higher levels of behavior theory. The most common theoretical constructs found in this sample are known to be efficacious elements in physical activity interventions. It is unclear, however, whether app designers consciously design physical activity mobile phone games with specific constructs in mind; it may be that games lend themselves well to inclusion of theory and any
Use of cooperative game theory in power system fixed-cost allocation
International Nuclear Information System (INIS)
Stamtsis, G.C.; Erlich, I.
2004-01-01
The use of cooperative game theory in power system fixed-cost allocation is investigated. The implementation of the allocation game in a bilateral transaction electricity market as well as in a pool market is discussed and the use of two well-known solution methods, nucleolus and the Shapley value, is explored. Conclusions are drawn which show that the Shapley value is a more preferable method when it is in the core of the game. For all the cases, results are illustrated in the IEEE 14-bus system. (author)
Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation
International Nuclear Information System (INIS)
Toledo, Porfirio
2013-01-01
We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games
Competition to commit crime: An economic experiment on illegal logging using behavioral game theory
Tananya Songchoo; Komsan Suriya
2012-01-01
This study constructs an economic experiment using behavioral game theory to figure out policies that discourage illegal logging in Thailand. A player is assigned to be either a police or an outlaw in the game. The game randomly matches two players in different roles. The lawbreaker can offer a bribe to police under uncertainties whether the police may refuse it or reject the offer because of too small amount of the bribe. Even when bribery is accepted, it is still uncertain for an lawbreaker...