Evolutionary Game Theory
Jörgen W. Weibull

August 1997
265 pp., 44 illus.

ISBN-10:
0-262-73121-5
ISBN-13:
978-0-262-73121-8


Table of Contents

Introduction
Acknowledgments
Mathematical Notation

1   Elements of Noncooperative Game Theory
1.1 Strategies and Payoff Functions
1.2 Dominance Relations and Best Replies
1.3 Nash Equilibrium
1.4 Refinements of Nash Equilibrium
1.5 Symmetric Two-Player Games

2   Evolutionary Stability Criteria
2.1 Evolutionarily Stable Strategies
2.2 Characterizations of ESS
2.3 Weaker Evolutionary Stablility Criteria
2.4 Setwise Evolutionary Stability Criteria
2.5 Social Efficiency in Doubly Symmetric Games
2.6 Preplay Communication
2.7 Role-Conditioned Behaviors

3   The Replicator Dynamics
3.1 Preliminaries
3.2 Dominated Strategies
3.3 Nash Equilibrium Strategies
3.4 Perfect Equilibrium Strategies
3.5 Evolutionarily and Neutrally Stable Strategies and Sets
3.6 Doubly Symmetric Games
3.7 Pure-Strategy Subsets Closed under Better Replies
3.8 Appendix

4   Other Selection Dynamics
4.1 Discrete-Time Versions of the Replicator Dynamics
4.2 The Replicator Dynamics in Cheap-Talk Games
4.3 General Selection Dynamics
4.4 Replication by Imitation

5   Multipopulation Models
5.1 Evolutionary Stability Criteria
5.2 The Standard and Adjusted n-Population Replicator Dynamics
5.3 Replication by Imitation
5.4 Replication by Contamination
5.5 Classes of Selection Dynamics
5.6 Implication of Evolutionary Dynamics for Noncooperative Solution Concepts
5.7 Robust Criteria for Evolutionary Dynamic Stability
5.8 Appendix

6   Elements of the Theory of Ordinary Differential Equations
6.1 Differential Equations and Vector Fields
6.2 The Induced Solution Mapping
6.3 Invariance and Stationarity
6.4 Stability Concepts
6.5 Lyapunov's Direct Method
6.6 Liouville's Formula

Bibliography

Index

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