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Evolutionary Game Theory and Evolutionary Stability

  1. Ross Cressman

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0309

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Cressman, R. 2011. Evolutionary Game Theory and Evolutionary Stability. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Wilfrid Laurier University, Department of Mathematics, Waterloo, Ontario, Canada

Publication History

  1. Published Online: 15 FEB 2011

Abstract

Evolutionary game theory is used to predict the behavior of individuals in populations (either of humans or other species) without relying on a detailed description of how these behaviors evolve over time (e.g., the replicator equation or the best response dynamics). For instance, if these behaviors correspond to a population state that satisfies the static payoff-comparison conditions of an evolutionarily stable strategy (ESS), then there is typically dynamic (i.e., evolutionary) stability at this state. We begin with a thorough summary of the evolutionary game theory perspective, when there is a finite set of (pure) strategies, for a symmetric two-player game in either normal or extensive form. The article then briefly discusses generalizations of evolutionary game theory, ESS, and evolutionary stability to several other classes of games. These include symmetric population games where payoffs to pure strategies are nonlinear functions of the current population state as well as asymmetric games where players are assigned different roles (e.g., two-role bimatrix games). Although terminology borrowed from evolutionary game theory applied to behaviors of individuals in biological species is used throughout, the concepts introduced are equally relevant in games modeling human behavior.

Keywords:

  • evolution;
  • game theory;
  • symmetric normal form;
  • payoff function;
  • bimatrix game