We study a setting where players are matched into pairs to play a Prisoners' Dilemma game. In the model presented, players are not rational; they simply imitate the more successful actions they observe. Furthermore, a certain correlation is added to the matching process: players that belong to a pair were both parties co-operate repeat partner next period whilst all other players are randomly matched into pairs. Although cooperation vanishes for any initial interior condition under complete random matching, the correlation in the matching process considered in this paper makes a significant amount of cooperation the unique outcome under mild conditions. Furthermore, it is shown that no separating equilibrium, i.e. a situation where cooperators and defectors are not matched together, exits
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