Evolutionary Dynamics and Extensive Form Games

327页

Economic Learning and Social Evolution General Editor
Ken Binmore, Director of the Economic Learning and Social Evolution Centre, University College London.
1. Evolutionary Games and Equilibrium Selection, Larry Samuelson,1997
2. The Theory of Learning in Games, Drew Fudenberg and David K. Levine, 1998
3. Game Theory and the Social Contract, Volume 2: Just Playing, Ken Binmore, 1998
4. Social Dynamics, Steven N. Durlauf and H. Peyton Young,editors, 2001
5. Evolutionary Dynamics and Extensive Form Games, Ross Cressman, 2003

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
vi Contents
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

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