| Series Foreword | xi |
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| Acknowledgments | xiii |
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| 1 | Introduction | 1 |
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| 1.1 | Introduction | 1 |
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| 1.2 | Large Populations and Matching Models | 4 |
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| 1.3 | Three Common Models of Learning and/or Evolution | 7 |
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| 1.4 | Cournot Adjustment | 8 |
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| 1.5 | Analysis of Cournot Dynamics | 9 |
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| 1.6 | Cournot Process with Lock-In | 10 |
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| 1.7 | Review of Finite Simultaneous-Move Games | 12 |
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| Appendix: Dynamical Systems and Local Stability | 24 |
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| References | 27 |
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| 2 | Fictitious Play | 29 |
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| 2.1 | Introduction | 29 |
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| 2.2 | Two-Player Fictitious Play | 30 |
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| 2.3 | Asymptotic Behavior of Fictitious Play | 32 |
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| 2.4 | Interpretation of Cycles in Fictitious Play | 35 |
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| 2.5 | Multiplayer Fictitious Play | 37 |
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| 2.6 | Payoffs in Fictitious Play | 39 |
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| 2.7 | Consistency and Correlated Equilibrium in Games with Two Strategies | 43 |
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| 2.8 | Fictitious Play and the Best-Response Dynamic | 44 |
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| 2.9 | Generalizations of Fictitious Play | 46 |
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| Appendix: Dirichlet Priors and Multinomial Sampling | 48 |
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| References | 49 |
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| 3 | Replicator Dynamics and Related Deterministic Models of Evolution | 51 |
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| 3.1 | Introduction | 51 |
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| 3.2 | Replicator Dynamics in a Homogenous Population | 53 |
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| 3.3 | Stability in the Homogenous-Population Replicator Dynamic | 55 |
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| 3.4 | Evolutionary Stable Strategies | 58 |
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| 3.5 | Asymmetric Replicator Models | 63 |
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| 3.6 | Interpretation of the Replicator Equation | 66 |
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| 3.7 | Generalizations of the Replicator Dynamic and Iterated Strict Dominance | 73 |
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| 3.8 | Myopic Adjustment Dynamics | 78 |
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| 3.9 | Set-Valued Limit Points and Drift | 83 |
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| 3.10 | Cheap Talk and the Secret Handshake | 89 |
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| 3.11 | Discrete-Time Replicator Systems | 91 |
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| Appendix: Liouville's Theorem | 95 |
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| References | 96 |
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| 4 | Stochastic Fictitious Play and Mixed-Strategy Equilibria | 101 |
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| 4.1 | Introduction | 101 |
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| 4.2 | Notions of Convergence | 102 |
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| 4.3 | Asymptotic Myopia and Asymptotic Empiricism | 103 |
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| 4.4 | Randomly Perturbed Payoffs and Smoothed Best Responses | 105 |
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| 4.5 | Smooth Fictitious Play and Stochastic Approximation | 110 |
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| 4.6 | Partial Sampling | 114 |
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| 4.7 | Universal Consistency and Smooth Fictitious Play | 117 |
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| 4.8 | Stimulus-Response and Fictitious Play as Learning Models | 121 |
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| 4.9 | Learning about Strategy Spaces | 128 |
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| Appendix: Stochastic Approximation Theory | 130 |
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| References | 133 |
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| 5 | Adjustment Models with Persistent Randomness | 137 |
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| 5.1 | Introduction | 137 |
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| 5.2 | Overview of Stochastic Adjustment Models | 138 |
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| 5.3 | Kandori-Mailath-Rob Model | 142 |
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| 5.4 | Discussion of Other Dynamics | 146 |
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| 5.5 | Local Interaction | 149 |
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| 5.6 | Radius and Coradius of Basins of Attraction | 154 |
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| 5.7 | Modified Coradius | 157 |
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| 5.8 | Uniform Random Matching with Heterogeneous Populations | 161 |
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| 5.9 | Stochastic Replicator Dynamics | 163 |
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| Appendix A: Review of Finite Markov Chains | 168 |
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| Appendix B: Stochastic Stability Analysis | 171 |
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| References | 173 |
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| 6 | Extensive-Form Games and Self-confirming Equilibrium | 175 |
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| 6.1 | Introduction | 175 |
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| 6.2 | An Example | 176 |
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| 6.3 | Extensive-Form Games | 178 |
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| 6.4 | A Simple Learning Model | 179 |
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| 6.5 | Stability of Self-confirming Equilibrium | 184 |
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| 6.6 | Heterogeneous Self-confirming Equilibrium | 185 |
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| 6.7 | Consistent Self-confirming Equilibrium | 186 |
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| 6.8 | Consistent Self-confirming Equilibria and Nash Equilibria | 188 |
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| 6.9 | Rationalizable SCE and Prior Information on Opponents' Payoffs | 191 |
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| References | 199 |
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| 7 | Nash Equilibrium, Large Population Models, and Mutations in Extensive-Form Games | 201 |
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| 7.1 | Introduction | 201 |
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| 7.2 | Relevant Information Sets and Nash Equilibrium | 202 |
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| 7.3 | Exogenous Experimentation | 203 |
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| 7.4 | Learning in Games Compared to the Bandit Problem | 207 |
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| 7.5 | Steady-State Learning | 213 |
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| 7.6 | Stochastic Adjustment and Backward Induction in a Model of "Fast-Learning" | 216 |
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| 7.7 | Mutations and Fast Learning in Models of Cheap Talk | 223 |
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| 7.8 | Experimentation and the Length of the Horizon | 226 |
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| Appendix: Review of Bandit Problems | 227 |
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| References | 229 |
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| 8 | Sophisticated Learning | 231 |
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| 8.1 | Introduction | 231 |
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| 8.2 | Three Paradigms for Conditional Learning | 233 |
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| 8.3 | Bayesian Approach to Sophisticated Learning | 235 |
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| 8.4 | Interpreting the Absolute Continuity Condition | 238 |
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| 8.5 | Choosing among Experts | 241 |
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| 8.6 | Conditional Learning | 243 |
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| 8.7 | Discounting | 247 |
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| 8.8 | Categorization Schemes and Cycles | 249 |
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| 8.9 | Introspective Classification Rules, Calibration, and Correlated Equilibrium | 254 |
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| 8.10 | Sonsino's Model of Pattern Recognition | 259 |
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| 8.11 | Manipulating Learning Procedures | 260 |
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| References | 266 |
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| Index | 269 |
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