Evolutionary Stability with Equilibrium Entrants

The strategy that upsets a potential evolutionarily stable strategy may in itself be very unstable, or may differ from the candidate strategy only in irrelevant ways. This paper develops a solution concept addressing these difficulties. We look for a set of Nash equilibria such that small groups of entrants whose members are satisfied with their entry cannot take the population out of the set. Such a set is robust to the iterated removal of weakly dominated strategies, depends only on the reduced normal form, and has the never a weak best response property. For generic two person extensive form games, such sets generate payoffs consistent with proper equilibria.