Cooperation, Imitation and Correlated Matching

We study a setting where imitative players are matched into pairs to play a Prisoners' Dilemma game. A well know result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we add a certain correlation to the matching process: players that belong to a pair were both parties cooperate repeat partner next period whilst all other players are randomly matched into pairs. This intuitive correlation introduced in the matching process makes cooperation the unique outcome in the long run under some conditions. Furthermore, we show that no assortative equilibrium exits.