Correlated equilibria and evolutionary stability

There is a considerable body of work which shows that the set of outcomes from rational play in a game is identical to a set of correlated equilibria. We show that the set of outcomes from evolutionary stable behavior, where nature serves as a correlating device, is identical to the set of strict correlated equilibria. This extends the result that ESS corresponds to strict Nash equilibrium, provided by R. Selten (Math. Social Sci. 5, 1983, 269–363), by allowing for correlation.