Do a Few Bad Apples Spoil the Barrel?: Community Enforcement with Incomplete Information
Abstract: We study the repeated prisonerís dilemma with random matching when some players may be "bad types" who never cooperate. We establish an anti-folk theorem: with anonymous players, cooperation is impossible in large groups under a smoothness assumption on the distribution of the number of bad types. Communities may avoid this grim outcome by segregating themselves into smaller sub-groups, at the cost of forgoing some gains from trade. Making players' identities observable does not help much: cooperation remains impossible in groups whose size N is large relative to the discount factor delta, in that (1-delta)*(sqrt of N) going to infinity. However, allowing within-match cheap talk supports cooperation in much larger groups: those where (1-delta)*(log of N) going to 0. Thus, in contrast to the situation where all players are rational, communication is essential for supporting cooperation in large groups in the presence of a few bad apples
