Evolutionary Stability in Games with Equivalent Strategies

Abstract

The first section briefly summarizes previous results in the literature. In the second section the concept of an Evolutionary Stable Strategy (ESS) is generalized for games with equivalent strategies. Dynamic stability results equivalent to the ones for the traditional definition of an ESS are proven. In the third section these results are applied to show that the assumption that types only use pure strategies can be relaxed to the case where types use finitely many different mixed strategies. In the fourth section, the results are used to give conditions for dynamic stability of populations playing asymmetric games.