Non-Cooperative Game Theory

2015-06-17
Non-Cooperative Game Theory

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  • Author: Takako Fujiwara-Greve
  • Publisher: Springer
  • ISBN: 4431556451
  • Category : Mathematics
  • Languages : en
  • Pages : 260

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) problems and possible remedies. The book contains many well-known games such as the prisoner’s dilemma, chicken (hawk–dove) game, coordination game, centipede game, and Cournot, Bertrand, and Stackelberg models in oligopoly. It also covers some advanced frameworks such as repeated games with non-simultaneous moves, repeated games with overlapping generations, global games, and voluntarily separable repeated prisoner’s dilemma, so that readers familiar with basic game theory can expand their knowledge. The author’s own research is reflected in topics such as formulations of information and evolutionary stability, which makes this book unique.

Dynamic Noncooperative Game Theory

1999-01-01
Dynamic Noncooperative Game Theory

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  • Author: Tamer Basar
  • Publisher: SIAM
  • ISBN: 089871429X
  • Category : Mathematics
  • Languages : en
  • Pages : 526

An overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and the role of different information patterns.

Value Solutions in Cooperative Games

2013-03-07
Value Solutions in Cooperative Games

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  • Author: Roger A McCain
  • Publisher: World Scientific
  • ISBN: 9814417416
  • Category : Business & Economics
  • Languages : en
  • Pages : 236

This book introduces new concepts for cooperative game theory, and particularly solutions that determine the distribution of a coalitional surplus among the members of the coalition. It also addresses several generalizations of cooperative game theory. Drawing on methods of welfare economics, new value solutions are derived for Non-Transferable Utility games with and without differences of bargaining power among the members of the coalition. Cooperation in intertemporal games is examined, and conditions that permit the reduction of these games to games in coalition function form are outlined. Biform games and games that combine non-cooperative search and matching of coalition members with cooperative solutions (i.e., efficient contracts) within the coalition are considered. Contents:Value Solutions for Superadditive Transferable Utility Games in Coalition Function FormZeuthen–Nash BargainingNontransferable Utility Games and Games in Partition Function FormA Shapley Value Algorithm for Games in Partition Function FormExtension of the Nucleolus to Nontransferable Utility Games in Partition Function FormA Core Imputation with Variable Bargaining PowerBargaining Power Biform GamesIntertemporal Cooperative Games: A Sketch of a TheoryA Theory of Enterprise Readership: Graduate students and researchers in the field of game theory. Keywords:Cooperative Games;Value;Imputation;Bargaining TheoryKey Features:Proposes a value solution for games of two or more players that: (i) is the Nash bargaining solution in a special case, (ii) allows for unsymmetrical bargaining power, (iii) allows for group-to-group bargaining, and (iv) is always a point in the core of the game if the game is not nullUses methods from mathematical welfare economics to bridge the gap from non-transferable utility to transferable utilityRelying on Biform Games (Brandenburger and Stuart), constructs a model of cooperative value creation in coalitions formed by non-cooperative search and matching

Computational Aspects of Cooperative Game Theory

2012
Computational Aspects of Cooperative Game Theory

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  • Author: Georgios Chalkiadakis
  • Publisher: Morgan & Claypool Publishers
  • ISBN: 1608456528
  • Category : Computers
  • Languages : en
  • Pages : 171

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 representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-used and practically important class of cooperative games that inherently have a natural compact representation. We investigate the complexity of solution concepts for such games, and generalizations of them. We briefly discuss games with non-transferable utility and partition function games. We then overview algorithms for identifying welfare-maximizing coalition structures and methods used by rational agents to form coalitions (even under uncertainty), including bargaining algorithms. We conclude by considering some developing topics, applications, and future research directions.

Foundations of Game Theory

2012-12-06
Foundations of Game Theory

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  • Author: Nicolai N. Vorob'ev
  • Publisher: Birkhäuser
  • ISBN: 3034885148
  • Category : Mathematics
  • Languages : en
  • Pages : 501

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. Kalkofen (on equilibrium selection). When the Russian edition was being written, these direc tions in game theory had not yet attained their final form, which appeared only in quite recent monographs; the present author has had to resist the temptation of attempting to produce an elementary exposition of the new theories for the English edition; readers of this edition will find only brief mention of the new material.

GAME THEORY

2013-03-01
GAME THEORY

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  • Author: Roger B. Myerson
  • Publisher: Harvard University Press
  • ISBN: 0674728610
  • Category : Business & Economics
  • Languages : en
  • Pages : 585

Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and methodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.

Game Theory

2015-03-30
Game Theory

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  • Author: Hans Keiding
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814623679
  • Category : Mathematics
  • Languages : en
  • Pages : 320

This book is intended as an introduction to game theory which goes beyond the field of application, economics, and which introduces the reader to as many different sides of game theory as possible within the limitations of an introduction. The main goal is to give an impression of the diversity of game theoretical models, while at the same time covering the standard topics. The book has an equal coverage of non-cooperative and cooperative games, and it covers several topics such as selecting Nash equilibria, non-transferable utility games, applications of game theory to logic, combinatorial and differential games.

Foundations of Non-cooperative Game Theory

2023
Foundations of Non-cooperative Game Theory

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  • Author: Klaus Ritzberger
  • Publisher:
  • ISBN: 9781383038590
  • Category : Game theory
  • Languages : en
  • Pages : 0

This textbook is intended for people taking advanced graduate courses in game theory. It provides a comprehensive account of the foundation theory and can be used in courses outside economics.

Game Theoretic Analysis

2019-10-14
Game Theoretic Analysis

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  • Author: Leon A Petrosyan
  • Publisher: World Scientific
  • ISBN: 9811202028
  • Category : Mathematics
  • Languages : en
  • Pages : 621

This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts.Part 1: Non-cooperative Games and Equilibrium AnalysisIn game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called 'coalitions') are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field.Part 2: Cooperative Games and Axiomatic ValuesIt is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field.

Game Theory and Economic Modelling

1990
Game Theory and Economic Modelling

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  • Author: David M. Kreps
  • Publisher: Oxford University Press
  • ISBN: 0198283814
  • Category : Mathematics
  • Languages : en
  • Pages : 204

Comprises lectures given at Tel Aviv University and Oxford University in 1990.