Observations on Cooperation

This paper develops a new theory of community enforcement that explains how cooperation can be sustained when agents change their partners over time. We study environments in which agents are randomly matched to play a Prisoner's Dilemma, and each player observes a few of the partner's past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes all previously proposed mechanisms for sustaining cooperation (e.g., contagious equilibria and belief-free equilibria). We present a novel, yet intuitive, combination of strategies that sustains cooperation in various environments. This mechanism is fully decentralized in the sense that each player's strategy conditions on only a few observations that the player makes regarding her current partner's past behavior. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.