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Evolution of Cooperation Through Imitation

David K. Levine and Wolfgang Pesendorfer

March 3,2001

Abstract: We study when cooperation and conflict emerge in games such as the Prisonerís Dilemma. We make use of two simple ideas: existing strategies are more likely to be imitated than new strategies are to be introduced, and prior to interaction it is possible to identify how an opponent will behave. We use methods introduced by Kandori, Mailath and Rob [1993] and Young [1993] 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, we characterize the degree of cooperation and conflict.