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This text offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception in biology in the 1970s through recent advances. Evolutionary game theory, which studies the behavior of large populations of strategically interacting agents, is used by economists to make predictions in settings where traditional assumptions about agents' rationality and knowledge may not be justified. Recently, computer scientists, transportation scientists, engineers, and control theorists have also turned to evolutionary game theory, seeking tools for modeling dynamics in multiagent systems. Population Games and Evolutionary Dynamics provides a point of entry into the field for researchers and students in all of these disciplines.

The text first considers population games, which provide a simple, powerful model for studying strategic interactions among large numbers of anonymous agents. It then studies the dynamics of behavior in these games. By introducing a general model of myopic strategy revision by individual agents, the text provides foundations for two distinct approaches to aggregate behavior dynamics: the deterministic approach, based on differential equations, and the stochastic approach, based on Markov processes. Key results on local stability, global convergence, stochastic stability, and nonconvergence are developed in detail. Ten substantial appendixes present the mathematical tools needed to work in evolutionary game theory, offering a practical introduction to the methods of dynamic modeling. Accompanying the text are nearly 200 color illustrations of the mathematics and theoretical results; many were created using the Dynamo software suite, which is freely available on the author's Web site. Readers are encouraged to use Dynamo to run quick numerical experiments and to create publishable figures for their own research.

William H. Sandholm is Professor of Economics at the University of Wisconsin–Madison.

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents in Brief......Page 6
Contents......Page 8
Series Foreword......Page 18
Preface......Page 20
1 Introduction......Page 30
I Population Games......Page 48
2 Population Games......Page 50
3 Potential Games, Stable Games, and Supermodular Games......Page 82
II Deterministic Evolutionary Dynamics......Page 146
4 Revision Protocols and Evolutionary Dynamics......Page 148
5 Deterministic Dynamics......Page 168
6 Best Response and Projection Dynamics......Page 206
III Convergence and Nonconvergence of Deterministic Dynamics......Page 248
7 Global Convergence of Evolutionary Dynamics......Page 250
8 Local Stability under Evolutionary Dynamics......Page 300
9 Nonconvergence of Evolutionary Dynamics......Page 348
IV Stochastic Evolutionary Models......Page 394
10 Stochastic Evolution and Deterministic Approximation......Page 396
11 Stationary Distributions and Infinite-Horizon Behavior......Page 426
12 Limiting Stationary Distributions and Stochastic Stability......Page 480
References......Page 570
Notation Index......Page 594
Index......Page 604
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