Game Theory

E. N. Barron 지음

Wiley 2024년 05월 13일 출간

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Authoritative and quantitative approach to modern game theory with applications from areas including economics, political science, computer science, and engineering Game Theory acknowledges the role of mathematics in making logical and advantageous decisions in adversarial situations and provides a balanced treatment of the subject that is both conceptual and applied. This newly updated and revised Third Edition streamlines the text to introduce readers to the basic theories behind games in a less technical but still mathematically rigorous way, with many new real-world examples from various fields of study, including economics, political science, military science, finance, biological science, and general game playing. The text introduces topics like repeated games, Bayesian equilibria, signaling games, bargaining games, evolutionary stable strategies, extensive games, and network and congestion games, which will be of interest across a wide range of disciplines. Separate sections in each chapter illustrate the use of Mathematica and Gambit software to create, analyze, and implement effective decision-making models. A companion website contains the related Mathematica and Gambit data sets and code. Solutions, hints, and methods used to solve most problems to enable self-learning are in an Appendix. Game Theory includes detailed information on: The von Neumann Minimax Theorem and methods for solving any 2-person zero sum matrix game. Two-person nonzero sum games solved for a Nash Equilibrium using nonlinear programming software or a calculus method. Nash Equilibria and Correlated Equilibria. Repeated games and punishment strategies to enforce cooperation Games in Extensive Form for solving Bayesian and perfect information games using Gambit. N-Person nonzero sum games, games with a continuum of strategies and many models in economics applications, duels, auctions, of Nash Equilibria, and the Stab

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Preface for the Third Edition xi Preface for the Second Edition xiii Preface for the First Edition xvi Acknowledgments xix Introduction xxi 1 Matrix Two-Person Games 1 1.1 What Is Game Theory? 1 1.2 Motivating Examples 2 1.2.1 Three Card Poker 3 1.2.2 Simplified Baseball 6 1.2.3 2 × 2 NIM 9 1.3 Mathematical Setup 11 1.3.1 Definition of a Matrix Game 11 1.3.2 Saddle Points: What It Means to be Optimal 14 Problems 15 1.4 Mixed Strategies 17 1.4.1 Definition of Mixed Strategies 17 1.4.2 Optimal Mixed Strategies 18 1.4.3 Best Response Strategies 23 1.4.4 Dominated Strategies 27 Problems 30 1.5 The Indifference Principle and Completely Mixed Games 32 1.5.1 2 × 2 Games 35 1.5.2 Completely Mixed Games and Invertible Matrix Games 37 1.5.3 An Application: Optimal Target Choice and Defense 40 Problems 45 1.6 Finding Saddle Points in General 49 1.6.1 Graphical Methods 49 1.6.2 The n × m Case and Linear Programming 52 1.6.3 Using Calculus 58 1.6.4 Symmetric Games 59 Problems 62 1.7 Existence of Saddle Points: The Von Neumann Minimax Theorem 67 1.7.1 Statement of the Minimax Theorem 67 1.7.2 Von Neumann’s Theorem Guarantees Matrix Games Have Saddle Points 69 Problems 69 1.8 Review Problems 75 Problems 75 1.9 Appendix: A Proof of the von Neumann Minimax Theorem 76 2 Two-Person Nonzero Sum Games 81 2.1 The Basics 81 2.1.1 Prisoner’s Dilemma 83 Problems 88 2.2 2 × 2 Bimatrix Games, Best Response, Equality of Payoffs 90 Problems 96 2.3 Interior Mixed Nash Points by Calculus 98 2.3.1 Calculus Method for Interior Nash 98 Problems 105 2.3.2 Existence of a Nash Equilibrium for Bimatrix Games 107 2.4 Nonlinear Programming Method for N

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저자(글) E. N. Barron