Evolutionary Cycles in Prisoners' Dilemma under Almost Public Monitoring

Abstract

We analyze the dynamics of cooperation in a repeated prisoner's dilemma under "almost public" monitoring, in which each player almost shares the same observation of each other's action, using replicator dynamics with mutations. Under "perfect" monitoring, where no player misperceives the opponent's action, only noncooperative strategies such as "always defect" and "never forgive if defected once" are known to survive. On the other hand, it is known that under near-public monitoring, the well-known tit-for-tat strategy (TFT) may form an equilibrium. Thus we investigated whether TFT survives under such a monitoring structure. As a result, we observe that TFT survives only in a limited range of parameters. Instead, we find that another strategy, Forgiver(FGV), in which a player punishes the opponent only once and then returns to cooperation, is the most abundant in a wider range of parameters.