Cooperation, imitation and partial rematching

We study a setting in which imitative players are matched into pairs to play a Prisonerʼs Dilemma game. A well-known result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we consider partial rematching: players that belong to a pair in which both parties cooperate repeat partner next period, while all other players are randomly matched into pairs. Under certain conditions, this rematching mechanism makes cooperation the unique outcome in the long run. Furthermore, we show that if imitation happens infrequently enough then cooperative behavior is always present in the population.