Table of Contents

1   Introduction

1.1 Introduction

1.2 Large Populations and Matching Models

1.3 Three Common Models of Learning and/or Evolution

1.4 Cournot Adjustment

1.5 Analysis of Cournot Dynamics

1.6 Cournot Process with Lock-in

1.7 Review of Finite Simultaneous-Move Games

Appendix: Dynamical Systems and Local Stability

References

2   Fictitious Play

2.1 Introduction

2.2 Two-Player Fictitious Play

2.3 Asymptotic Behavior of Fictitious Play

2.4 Interpretation of Cycles in Fictitious Play

2.5 Multiplayer Fictitious Play

2.6 Payoffs in Fictitious Play

2.7 Consistency and Correlated Equilibrium in Games with Two Strategies

2.8 Fictitious Play and the Best-Response Dynamic

2.9 Generalizations of Fictitious Play

Appendix: Dirichlet Priors and Multinomial Sampling

References

3   Replicator Dynamics and Related Deterministic Models of Evolution

3.1 Introduction

3.2 Replicator Dynamics in a Homogeneous Population

3.3 Stability in the Homogeneous-Population Replicator Dynamic

3.4 Evolutionarily Stable Strategies

3.5 Asymmetric Replicator Models

3.6 Interpretation of the Replicator Equation

3.7 Generalizations of the Replicator Dynamic and Iterated Strict Dominance

3.8 Myopic Adjustment Dynamics

3.9 Set-Valued Limit Points and Drift

3.10 Cheap Talk and the Secret Handshake

3.11 Discrete-Time Replicator Systems

Appendix: Liouville's Theorem

References

4   Stochastic Fictitious Play and Mixed-Strategy Equilibria

4.1 Introduction

4.2 Notions of Convergence

4.3 Asymptotic Myopia and Asymptotic Empiricism

4.4 Randomly Perturbed Payoffs and Smoothed Best Responses

4.5 Smooth Fictitious Play and Stochastic Approximation

4.6 Partial Sampling

4.7 Universal Consistency and Smooth Fictitious Play

4.8 Stimulus-Response and Fictitious Play as Learning Models

4.9 Learning about Strategy Spaces

Appendix: Stochastic Approximation Theory

References

5   Adjustment Models with Persistent Randomness

5.1 Introduction

5.2 Overview of Stochastic Adjustment Models

5.3 Kandori-Mailath-Rob Model

5.4 Discussion of Other Dynamics

5.5 Local Interaction

5.6 Radius and Coradius of Basins of Attraction

5.7 Modified Coradius

5.8 Uniform Random Matching with Heterogeneous Populations

5.9 Stochastic Replicator Dynamics

Appendix A: Review of Finite Markov Chains

Appendix B: Stochastic Stability Analysis

References

6   Extensive-Form Games and Self-confirming Equilibrium

6.1 Introduction

6.2 An Example

6.3 Extensive-Form Games

6.4 A Simple Learning Model

6.5 Stability of Self-confirming Equilibrium

6.6 Heterogeneous Self-confirming Equilibrium

6.7 Consistent Self-confirming Equilibrium

6.8 Consistent Self-confirming Equilibria and Nash Equilibria

6.9 Rationalizable SCE and Prior Information on Opponents' Payoffs

References

7   Nash Equilibrium, Large Population Models, and Mutations in Extensive-Form Games

7.1 Introduction

7.2 Relevant Information Sets and Nash Equilibrium

7.3 Exogenous Experimentation

7.4 Learning in Games Compared to the Bandit Problem

7.5 Steady-State Learning

7.6 Stochastic Adjustment and Backward Induction in a Model of "Fast Learning"

7.7 Mutations and Fast Learning in Models of Cheap Talk

7.8 Experimentation and the Length of the Horizon

Appendix: Review of Bandit Problems

References

8   Sophisticated Learning

8.1 Introduction

8.2 Three Paradigms for Conditional Learning

8.3 Bayesian Approach to Sophisticated Learning

8.4 Interpreting the Absolute Continuity Condition

8.5 Choosing among Experts

8.6 Conditional Learning

8.7 Discounting

8.8 Categorization Schemes and Cycles

8.9 Introspective Classification Rules, Calibration, and Correlated Equilibrium

8.10 Sonsino's Model of Pattern Recognition

References