Evolutionary stability in extensive two-person games

Abstract

The concept of an ESS (evolutionary stable strategy) has been introduced by Maynard Smith and Price for two-person games in normal form (Maynard Smith and Price, 1973). The generalization to extensive two-person games raises various conceptual and mathematical problems, like the notion of symmetry in such games. A direct translation of the normal form concept to the framework of extensive games leads to unsatisfactory consequences. Therefore, on the basis of the trembling hand approach to perfectness (Selten, 1975), the notion of a limit ESS is introduced. Several theorems on the properties of a limit ESS provide tools for the analysis of specific games. Finally, a many-period model of animal contests with ritual fights and escalated conflicts is investigated in detail.