Evolution and Mixed Strategies |
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Authors: | Ken Binmore Larry Samuelson |
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Institution: | a Department of Economics, University College London, Gower Street, London, WC1E 6BT, United Kingdom;b Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, Wisconsin, 53706 |
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Abstract: | Selten (1980, J. Theoret. Biol., 84, 93–101) showed that no mixed equilibria are evolutionarily stable when players can condition their strategies on their roles in a game. Alternatively, Harsanyi's (1973, Int. J. Game Theory, 2, 1–23) purification argument implies that all mixed equilibria are approximations of strict, and hence evolutionarily stable, equilibria of games with slightly perturbed payoffs. This paper reconciles these results: Approximations of mixed equilibria have high invasion barriers, and hence are likely to persist, when payoff perturbations are relatively important and role identification is relatively noisy. When payoff perturbations are unimportant and role identification is precise, approximations of mixed equilibria will have small invasion barriers and are unlikely to persist. Journal of Economic Literature Classification Numbers: C70, C78. |
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Keywords: | evolutionary stability ESS mixed strategy asymmetric game |
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