On the Interpretation of Evolutionary Stable Sets

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.