Evolutionary stability in general extensive-form games of perfect information

Zibo Xu

We consider a basic dynamic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. A state is evolutionarily stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. We prove that, for all finite extensive-form games of perfect information, only Nash equilibria are evolutionarily stable. We show that, in games where a player may play at more than one node along some path, even when the populations increase to infinity, there may be some evolutionarily stable states which are not part of the backward induction equilibrium component. We give a sufficient condition for evolutionary stability and show how much extra value is needed in the terminal payoffs to make an equilibrium evolutionarily stable.

January, 2013