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

Author

Listed:
  • Takuo Sugaya
  • Alexander Wolitzky

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.

Suggested Citation

  • Takuo Sugaya & Alexander Wolitzky, 2020. "A Few Bad Apples Spoil the Barrel: An Anti-folk Theorem for Anonymous Repeated Games with Incomplete Information," American Economic Review, American Economic Association, vol. 110(12), pages 3817-3835, December.
    • Handle: RePEc:aea:aecrev:v:110:y:2020:i:12:p:3817-35
    DOI: 10.1257/aer.20200068
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    Cited by:

    1. Sugaya, Takuo & Wolitzky, Alexander, 2023. "Bad apples in symmetric repeated games," Theoretical Economics, Econometric Society, vol. 18(4), November.
    2. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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