Evolutionarily stable sets in symmetric extensive two-person games

Evolutionarily stable (ES) sets are characterized for evolutionary games in extensive form. It is shown that, for the normal form of games involving informational symmetries or repeated play, the standard approach of determining evolutionarily stable strategies (ESSs) often fails to predict the evolutionary outcome. The dynamic stability of ES sets is proved in both the pure strategy and mixed strategy models. ES sets are shown to also generalize the notion of direct ESSs (an earlier attempt to apply ESS theory to extensive games). The theory is illustrated by three examples of biological games in extensive form.