Evolutionarily Stable Strategy Distributions for the Repeated Prisonerʹs Dilemma

This paper introduces the idea of anevolutionarily stable strategy distribution, which generalizes the idea of an evolutionarily stable strategy; roughly speaking, an evolutionarily stable strategy distribution is a finite set of symbiotic strategies which is unaffected by low levels of mutation. This idea is then applied to then-person Repeated Prisonerʹs Dilemma, of which the usual Repeated Prisonerʹs Dilemma is the special casen=2. Given some standard assumptions on what mutations are possible, it is shown that if the probability of future interactions is sufficiently large, there are no evolutionarily stable strategy 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.