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  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
Creation-Date: May 1995
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