Evolution and Strategic Stability: From Maynard Smith to Kohlberg and Mertens*

While strategic stability (Kohlberg and Mertens [4]) is mathematically elegant, it is not yet fully understood when or why it is a reasonable condition on a set of equilibria. Cho and Kreps [ 1, p. 2203 conclude “... if there is an intuitive story to go along with the full strength of stability, it is beyond our powers to offer it here.” Elaborate refinements of Nash equilibrium motivated by considerations of rational play have in general come to be viewed with increasing skepticism. When a given game is played repeatedly by anonymous, randomly matched players from a large population of potential players, there is the opportunity for learning or “evolution” without the difficulty of supergame effects. Evolutionary stability (Maynard Smith [S]) is essentially a condition that there be no profitable entry opportunities given the actions of the incumbent population. A remarkable result (due to van Damme [S] ) shows that evolutionarily stable strategies generate proper equilibria (Myerson [6]). Thus, a rather strong solution concept can be motivated not as an implication of rational play, but instead as a necessary condition for the robustness of a society’s behavior in the face of small groups of entrants playing alternate strategies. This paper presents such a result, but one that is considerably stronger in two ways. First, we work with a much weaker solution concept. Some