Evolutionarily stable sets

This paper provides definitions for the evolutionary stability of sets of s trategies based on simple fitness comparisons in the spirit of the definiti on of an evolutionarily, stable strategy (ESS) by Taylor and Jonker (1978). It compares these with the set-valued notions of Thomas (1985d) and Swinke ls (1992). Provided only that the fitness function is analytic, our approac h yields an alternative characterization of Thomas' evolutionarily stable s ets (ES Sets) which does not rely on the structure or topology of the under lying strategy space. Moreover, these sets are shown to have a very special geometric structure and to be finite in number. For bimatrix games ES Sets are shown to be more uniformly robust against mutations than apparent from the definition and hence to be equilibrium evolutionarily stable sets in t he sense of Swinkels (1992).