American Economic Review
ISSN 0002-8282 (Print) | ISSN 1944-7981 (Online)
A Few Bad Apples Spoil the Barrel: An Anti-folk Theorem for Anonymous Repeated Games with Incomplete Information
American Economic Review
vol. 110,
no. 12, December 2020
(pp. 3817–35)
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.Citation
Sugaya, Takuo, and Alexander Wolitzky. 2020. "A Few Bad Apples Spoil the Barrel: An Anti-folk Theorem for Anonymous Repeated Games with Incomplete Information." American Economic Review, 110 (12): 3817–35. DOI: 10.1257/aer.20200068Additional Materials
JEL Classification
- C72 Noncooperative Games
- C73 Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
- D83 Search; Learning; Information and Knowledge; Communication; Belief; Unawareness