Cooperation, competition, and welfare in a matching market

We investigate the welfare effect of increasing competition in an anonymous two-sided matching market, where matched pairs play an infinitely repeated Prisoner's Dilemma. Higher matching efficiency is usually considered detrimental as it creates stronger incentives for defection. We point out, however, that a reduction in matching frictions also increases welfare because more agents find themselves in a cooperative relationship. We characterize the conditions for which increasing competition increases overall welfare. In particular, this is always the case when the incentives for defection are high.