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

Kuzmics C. On the elimination of dominated strategies in stochastic models of evolution with large populations. Games and Economic Behavior. 2011;72(2):452-466.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)