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On the elimination of dominated strategies in stochastic models of evolution with large populations

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  • Kuzmics, Christoph

Abstract

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W).

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  • Kuzmics, Christoph, 2011. "On the elimination of dominated strategies in stochastic models of evolution with large populations," Games and Economic Behavior, Elsevier, vol. 72(2), pages 452-466, June.
    • Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:452-466
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