EVOLUTIONARILY STABLE STRATEGY DISTRIBUTIONS FOR THE REPEATED PRISONERS-DILEMMA

This paper introduces the idea of an evolutionarily stable strategy di stribution, which generalizes the idea of an evolutionarily stable str ategy; roughly speaking, an evolutionarily stable strategy distributio n is a finite set of symbiotic strategies which is unaffected by low l evels of mutation. This idea is then applied to the n-person Repeated Prisoner's Dilemma, of which the usual Repeated Prisoner's Dilemma is the special case n = 2. Given some standard assumptions on what mutati ons are possible, it is shown that if the probability of future intera ctions is sufficiently large, there are no evolutionarily stable strat egy distributions. (And hence no evolutionarily stable strategies.) An example is given of an evolutionarily stable strategy distribution in the case when the set of possible mutant strategies is restricted. (C ) 1997 Academic Press Limited.