【经典】Evolutionary Dynamics and Extensive Form Games

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收藏 2008-11-07

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ISBN-10:0-262-03305-4 ISBN-13:978-0-262-03305-3 About the Author： Ross Cressman is Professor of Mathematics at Wilfrid Laurier University, Canada. Endorsements "This book extends the study of evolutionary dynamics to extensive form games, shifting seamlessly between biological foundations, mathematical tools, and economic applications. It will be an essential resource for anyone interested in the evolutionary foundations of behavior." —Larry Samuelson, Department of Economics, University of Wisconsin, Madison "The first hundred pages of this book form the best and most elegant introduction to evolutionary game theory I have ever come across. What follows is an admirable monograph on extensive &nbsp;&nbsp;form games, an essential part of game theory that has so far resisted invasion attempts by evolutionary methods. Under Cressman's assault, the citadel has fallen. This superb achievement is a landmark in the development of evolutionary game theory." —Karl Sigmund, Institute of Mathematics, University of Vienna CONTENTS: Series Foreword ix Preface xi 1 Introduction 1 1.1 Extensive Form versus Normal Form 2 1.2 Biology versus Economics 8 1.3 Imitation 12 1.4 Organizational Matters 15 1.5 Notes 16 2 Symmetric Normal Form Games 19 2.1 The Replicator Dynamic 19 2.2 Dynamics for Two-Strategy Games 23 2.3 Monotone Selection Dynamics 27 2.4 Fictitious Play and Best Response Dynamic 31 2.5 Convergence and Stability: NE and ESS 34 2.6 Three-Strategy Game Dynamics 37 2.6.1 Rock–Scissors–Paper Games 37 2.6.2 ESSets and NE Components 42 2.6.3 More Three-Strategy Games 43 2.7 Dynamic Stability for General Games 46 2.8 Natural Selection at a Single Locus 53 2.8.1 Discrete-Time Viability Selection 53 2.8.2 Continuous-Time Natural Selection 54 2.9 One-Stage Simultaneity Games 56 2.10 Multi-armed Bandits 58 2.11 Appendix 64 2.12 Notes 66 3 Bimatrix Games 69 3.1 Nash Equilibria and Strict Equilibrium Sets 70 3.2 Bimatrix Replicator and Best Response Dynamics 71 3.2.1 The Owner-Intruder Game 74 3.3 Dynamics for Two-Strategy Bimatrix Games 75 3.3.1 Nondegenerate Bimatrix Games 76 3.3.2 Degenerate Bimatrix Games 79 3.4 Symmetrized Bimatrix Games 85 3.4.1 The Symmetrized Bimatrix Replicator Dynamic 88 3.4.2 The Symmetrized Best Response Dynamic 93 3.5 Bimatrix Monotone Selection Dynamics 96 3.6 Notes 101 4 Asymmetric Games 103 4.1 The Normal Form 104 4.2 The Extensive Form: NE and ESSets 106 4.2.1 An Age-Structured Owner-Intruder Game 108 4.3 SESets and Agent Normal Forms 110 4.4 Dynamics and the Wright Manifold 113 4.4.1 The Replicator Dynamic and Subgames 114 4.4.2 Best Response Dynamics 116 4.5 Truly Asymmetric Two-Player Games 117 4.5.1 The Age-Structured Owner-Intruder Game Dynamic 121 4.6 Truly Symmetric Two-Player Games 123 4.6.1 A Truly Symmetric Game Dynamic Counterexample 125 4.6.2 Parallel Bandits 128 4.7 Asymmetric Games with Two Roles 137 4.7.1 A Family of Asymmetric Games 137 4.7.2 Two-Species Evolutionarily Stable Strategies 140 4.8 A Hierarchical Hawk-Dove Game 146 4.9 Appendix A 150 4.10 Appendix B 152 4.11 Notes 153 5 Natural Selection with Multiple Loci 155 5.1 Continuous-Time Selection-Recombination 155 5.2 Symmetric Extensive Form with Additive Fitness 157 5.3 Recombination 160 5.4 Selection and Recombination 162 5.5 Notes 163 6 Extensive Form Games 165 6.1 N-Player Extensive Form Games 166 6.1.1 Strategies and Payoffs 168 6.1.2 Nash Equilibria, Subgames, and Backward Induction 171 6.2 Normal Forms and the Replicator Dynamic 173 6.3 TheWright Manifold and Replicator Dynamic 175 6.4 Symmetric Extensive Form Games 180 6.5 Appendix 184 6.6 Notes 185 7 Simultaneity Games 187 7.1 Elementary Two-Stage Simultaneity Games 188 7.2 Two-Stage Two-Strategy Games 192 7.2.1 Two-Stage Two-Strategy Repeated Games 195 7.2.2 Symmetric Signaling Games 197 7.2.3 Cheap Talk Games 200 7.3 Asymptotic Stability of Pervasive NE 201 7.3.1 Simultaneity Games with No Asymmetric Subgames 201 7.3.2 Simultaneity Games with Asymmetric Subgames 204 7.3.3 Simultaneity Games with Moves by Nature 206 7.4 TheWar of Attrition 207 7.4.1 The Discrete War of Attrition 208 7.4.2 The Continuous War of Attrition 213 7.4.3 The Discrete War of Aggression 215 7.5 The Finitely Repeated Prisoner’s Dilemma Game 217 7.5.1 The Replicator and Monotone Selection Dynamics 220 7.5.2 The Best Response Dynamic and Fictitious Play 222 7.6 Appendix A: Proof of Theorem 7.5.3 228 7.7 Appendix B: Maximal Attractor 232 7.8 Notes 233 8 Perfect Information Games 235 8.1 Elementary Perfect Information Games 237 8.2 Equilibrium Selection: Dynamic Approach 240 8.2.1 The Replicator and Monotone Selection Dynamics 242 8.2.2 Fictitious Play and Best Response Dynamic 248 8.2.3 Behavior Strategy Fictitious Play 252 8.3 The Centipede Game 255 8.3.1 Centipede Games of Lengths Two and Three 256 8.3.2 Centipede Games of Length N ≥ 4 258 8.4 Extensive &nbsp;&nbsp;Form Bandits 260 8.4.1 The Centipede Bandit 268 8.5 Appendix A 276 8.6 Appendix B 283 8.7 Notes 287 9 Subgame Monotonicity 289 9.1 Monotone Trajectories 289 9.2 Subgame Monotone Trajectories 292 9.3 An Imitation Example 301 9.4 Discussion 303 9.5 Notes 304 Bibliography 307 Index