A Few Bad Apples Spoil the Barrel: An Anti-Folk Theorem for Anonymous Repeated Games with Incomplete Information

A Few Bad Apples Spoil the Barrel: An Anti-Folk Theorem for Anonymous Repeated Games with Incomplete Information

By
Takuo Sugaya, Alexander Wolitzky
American Economic Review. December
2020, Vol. 110, Issue 12, Pages 3817–3835

We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner’s dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases.