Evolutionary game theory:
Evolutionary game theory (EGT) is the application of interaction dependent strategy drift in populations to game theory. It originated in 1973 with John Maynard Smith and George R. Price's formalization of evolutionary stable strategies as an application of the mathematical theory of games to biological contexts, arising from the realization that frequency dependent fitness introduces a strategic aspect to evolution. EGT differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria. Despite its name, evolutionary game theory has become of increased interest to economists, sociologists, anthropologists, and philosophers.
The common methodology to study the evolutionary dynamics in games is through replicator equations. Continuous replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true. The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states.
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[edit] References
- Maynard Smith, J. (1982) Evolution and the Theory of Games.
- P. Hammerstein and R. Selten, "Game theory and evolutionary biology", in Handbook of Game Theory with Economic Applications, R. J. Aumann and S. Hart, Eds. (Elsevier, Amsterdam, 1994), vol. 2, pp. 929-993
- Hofbauer, J. and Sigmund, K. (1998) Evolutionary games and population dynamics, Cambridge University Press
- Taylor, P. D. (1979). Evolutionarily Stable Strategies with Two Types of Players J. Appl. Prob. 16, 76-83.
- Taylor, P. D., and Jonker, L. B. (1978). Evolutionarily Stable Strategies and Game Dynamics Math. Biosci. 40, 145-156.
- Weibull, J. W. (1995) Evolutionary game theory, MIT Press
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