Uniform barriers and evolutionarily stable sets

Immanuel M. Bomze

pp. 225-243

in: Werner Leinfellner, Eckehart Köhler (eds), Game theory, experience, rationality, Berlin, Springer, 1998

Abstract

A key concept in evolutionary game theory is that of evolutionary stability [21, 20]. Originally defined for pairwise contests, i.e. symmetric two-person games, a mixed strategy x is said to be evolutionarily stable if it is a best reply to itself, and, moreover, is a better reply to any alternative best reply y than this is to itself. It has been shown that evolutionary stability has important implications for population dynamics based on evolutionary selection. In particular, an evolutionarily stable strategy, viewed as a population state in a finite game in which individuals are "programmed" to pure strategies, is asymptotically stable in the corresponding replicator dynamics [26].