Community enforcement when players observe partners' past play

I investigate whether a community can sustain cooperation in the repeated prisoner’s dilemma by having cheaters punished not by their victims but by third parties. Motivated by systems of credit history reporting, online feedback, and some experimental settings, I assume that players can access information about their partners’ past play for free, but acquiring information about their partners’ past partners’ past play is prohibitively costly. In this setting, even though players cannot distinguish cheaters from those who punish cheaters, I show that any level of cooperation can be sustained by an equilibrium. The equilibrium I construct has the following two properties: players choose their actions independently of their own past play, and they are indifferent between cooperation and defection at all histories. This equilibrium carries over to the finite-population setting and is robust to noise in the process of choosing actions or of recording past play. ∗I am grateful to Drew Fudenberg and Attila Ambrus for their guidance. I am also grateful to Nabil Al-Najjar, Carlos Alós-Ferrer, Sylvain Chassang, Bo Chen, Alex Gelber, Jerry Green, Fuhito Kojima, George Mailath, Mihai Manea, Andrew Marder, Parag Pathak, Charles Roddie, Tiantian Qiu, Tadashi Sekiguchi, Yeneng Sun, Yuichi Yamamoto, seminar participants at various places, the Associate Editor, and two anonymous referees for their helpful comments. †Affiliation: Department of Economics, Princeton University. E-mail address: [email protected]