Evolutionary stability in the repeated prisoner's dilemma

Abstract Recently, biologists have explored evolutionary explanations of apparently altruistic behavior in situations of conflict, often modeled as the “Prisoner's Dilemma.” Certain simple cooperative strategies, notably TIT-FOR-TAT, have been successful in computer simulations of the evolution of populations of individuals who interact according to the Prisoner's Dilemma. Some attempts to formalize this have used the concept of “evolutionary stability.” But Boyd and Lorberbaum (1987 , Nature (London) 327 , 58–59) recently showed that no single pure strategy (such as TIT-FOR-TAT) can be evolutionarily stable. We extend their argument to derive a more powerful result, which implies, first, that no finite mixture of pure strategies can be evolutionarily stable, and, second, that no mixture of TIT-FOR- n -TATS can be evolutionarily stable. We interpret our negative results to suggest that evolutionary stability is too demanding a criterion.