A Few Bad Apples Spoil the Barrel: An Anti-folk Theorem for Anonymous Repeated Games with Incomplete Information
Takuo Sugaya, Alexander Wolitzky
American Economic Review · 2020 · Volume 110 · Issue 12
Abstract
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.
Keywords
Noncooperative Games, Stochastic and Dynamic Games, Evolutionary Games, Repeated Games, Search, Learning, Information and Knowledge, Communication, Belief, Unawareness
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