Theory of Learning in Games

ISBN-10: 0262061945
ISBN-13: 9780262061940
Edition: 1998
List price: $55.00
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Description: Here the authors develop the explanation that equilibrium in games arises as the long-run outcome of a process in which less than fully rational players grope for optimality over time. Ways are suggested for economists to modify traditional concepts.

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Book details

List price: $55.00
Copyright year: 1998
Publisher: MIT Press
Publication date: 6/3/1998
Binding: Hardcover
Pages: 292
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.606
Language: English

Here the authors develop the explanation that equilibrium in games arises as the long-run outcome of a process in which less than fully rational players grope for optimality over time. Ways are suggested for economists to modify traditional concepts.

Drew Fudenberg is Professor of Economics at MIT.

David K. Levine is John H. Biggs Distinguished Professor of Economics at Washington University, St. Louis.

Series Foreword
Acknowledgments
Introduction
Introduction
Large Populations and Matching Models
Three Common Models of Learning and/or Evolution
Cournot Adjustment
Analysis of Cournot Dynamics
Cournot Process with Lock-In
Review of Finite Simultaneous-Move Games
Appendix: Dynamical Systems and Local Stability
References
Fictitious Play
Introduction
Two-Player Fictitious Play
Asymptotic Behavior of Fictitious Play
Interpretation of Cycles in Fictitious Play
Multiplayer Fictitious Play
Payoffs in Fictitious Play
Consistency and Correlated Equilibrium in Games with Two Strategies
Fictitious Play and the Best-Response Dynamic
Generalizations of Fictitious Play
Appendix: Dirichlet Priors and Multinomial Sampling
References
Replicator Dynamics and Related Deterministic Models of Evolution
Introduction
Replicator Dynamics in a Homogenous Population
Stability in the Homogenous-Population Replicator Dynamic
Evolutionary Stable Strategies
Asymmetric Replicator Models
Interpretation of the Replicator Equation
Generalizations of the Replicator Dynamic and Iterated Strict Dominance
Myopic Adjustment Dynamics
Set-Valued Limit Points and Drift
Cheap Talk and the Secret Handshake
Discrete-Time Replicator Systems
Appendix: Liouville's Theorem
References
Stochastic Fictitious Play and Mixed-Strategy Equilibria
Introduction
Notions of Convergence
Asymptotic Myopia and Asymptotic Empiricism
Randomly Perturbed Payoffs and Smoothed Best Responses
Smooth Fictitious Play and Stochastic Approximation
Partial Sampling
Universal Consistency and Smooth Fictitious Play
Stimulus-Response and Fictitious Play as Learning Models
Learning about Strategy Spaces
Appendix: Stochastic Approximation Theory
References
Adjustment Models with Persistent Randomness
Introduction
Overview of Stochastic Adjustment Models
Kandori-Mailath-Rob Model
Discussion of Other Dynamics
Local Interaction
Radius and Coradius of Basins of Attraction
Modified Coradius
Uniform Random Matching with Heterogeneous Populations
Stochastic Replicator Dynamics
Review of Finite Markov Chains
Stochastic Stability Analysis
References
Extensive-Form Games and Self-confirming Equilibrium
Introduction
An Example
Extensive-Form Games
A Simple Learning Model
Stability of Self-confirming Equilibrium
Heterogeneous Self-confirming Equilibrium
Consistent Self-confirming Equilibrium
Consistent Self-confirming Equilibria and Nash Equilibria
Rationalizable SCE and Prior Information on Opponents' Payoffs
References
Nash Equilibrium, Large Population Models, and Mutations in Extensive-Form Games
Introduction
Relevant Information Sets and Nash Equilibrium
Exogenous Experimentation
Learning in Games Compared to the Bandit Problem
Steady-State Learning
Stochastic Adjustment and Backward Induction in a Model of "Fast-Learning"
Mutations and Fast Learning in Models of Cheap Talk
Experimentation and the Length of the Horizon
Appendix: Review of Bandit Problems
References
Sophisticated Learning
Introduction
Three Paradigms for Conditional Learning
Bayesian Approach to Sophisticated Learning
Interpreting the Absolute Continuity Condition
Choosing among Experts
Conditional Learning
Discounting
Categorization Schemes and Cycles
Introspective Classification Rules, Calibration, and Correlated Equilibrium
Sonsino's Model of Pattern Recognition
Manipulating Learning Procedures
References
Index

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