The evolutionary robustness of forgiveness and cooperation

We study the evolutionary robustness of strategies in in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator dynamics. We show that there are strategies with a uniformly large basin of attraction independent of the size of the population. Moreover, we show that those strategies forgive defections and, assuming that they are symmetric, they cooperate. We provide partial efficiency results for asymmetric strategies.