Cooperation in the sporadically repeated prisoners’ dilemma via reputation mechanisms

We consider the sporadically repeated Prisoners’ Dilemma, examine a class of two-state reputation mechanisms and find that only three have efficient robust perfect Nash equilibria in Markov strategies. Since the asymptotic stability properties are crucial to their plausibility as realistic solutions, we examine replicator dynamics for the simplest reputation mechanism that entails both punishment and penitence. The strategy to cooperate with Good opponents and defect against Bad opponents is a global attractor of replicator dynamics, and hence cooperation is successfully sustained in the long run.