SFB 303 Discussion Paper No. B - 313

Author: Balkenborg, Dieter, and Karl H. Schlag
Title: On the Interpretation of Evolutionary Stable Sets
Abstract: We call a set of strategies "uniformly evolutionary stable" if the following holds after a small mutation of a monomorphic population playing a strategy in the set: a) No mutant strategy can spread. b) Mutant strategies not in the set will be driven out. c) The meaning of a "small mutation" can be chosen independently of both the mutant and the incumbent strategy. We consider our notion an intuitive extension of the concept of an evolutionarily stable strategy. We show that our notion coincides with the notion of evolutionarily stable sets due to Thomas [22] in the case of bimatrix games, but it is stronger in general. As an application we study uniformly evolutionarily stable sets in truly asymmetric contest.
Keywords: evolutionarily stable set, evolutionarily stable strategy, neutral stability, strict equilibrium, mixed strategy model, asymmetric contest
JEL-Classification-Number: C79
Creation-Date: May 1995
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