The Evolution of Cooperation Through Imitation
We study when cooperation and conflict emerge in a class of “folk theorem” games such as the Prisoner’s Dilemma. We make use of two simple ideas: existing strategies are more likely to be imitated than new strategies are to be introduced, and it is possible to identify how an opponent will behave prior to the interaction. Both global interactions and the local interaction model of Ellison  are examined. We use methods introduced by Kandori, Mailath and Rob  and Young  to examine the long-run evolutionary limit of this system. This limit contains only pure strategies. A sufficient condition for a unique limit is that a strategy beat all others in pairwise contests. When players can perfectly determine the strategy used by their opponent, full cooperation is achieved. When identification is imperfect, the long-run limit can be interpreted as a model of endogenous preferences where players who appear similar are treated altruistically, and players who appear to be different are treated spitefully.