A knowledge of the conditions under which natural selection can favour cooperative behaviour among unrelated individuals is crucial for understanding the evolution of social behaviour, particularly among humans and other social mammals. In an influential1-5 series of works, Axelrod6-10 has argued that reciprocal cooperation is likely to evolve when individual organisms interact repeatedly. This conclusion is based, in part, on an evolutionary analysis of the repeated Prisoner's Dilemma game which indicates that strategies which lead to reciprocal cooperation are evolutionarily stable1,11. In this paper, however, we argue that no pure strategy can be evolutionarily stable in this game. This fact casts doubt on several of Axelrod's conclusions about the evolution of reciprocity.
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