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Bad apples in symmetric repeated games

Author

Listed:
  • Sugaya, Takuo

    (Graduate School of Business, Stanford University)

  • Wolitzky, Alexander

    (Department of Economics, MIT)

Abstract

We study large-population repeated games where players are symmetric but not anonymous, so player-specific rewards and punishments are feasible. Players may be commitment types who always take the same action. Even though players are not anonymous, we show that an anti-folk theorem holds when the commitment action is "population dominant," meaning that it secures a payoff greater than the population average payoff. For example, voluntary public goods provision in large populations is impossible when commitment types never contribute, even if monetary rewards can be targeted to contributors; however, provision is possible if non-contributors can be subjected to involuntary fines. A folk theorem under incomplete information provides a partial converse to our result. Along the way, we develop some general results on symmetric games with incomplete information and/or repeated play.

Suggested Citation

  • Sugaya, Takuo & Wolitzky, Alexander, 2023. "Bad apples in symmetric repeated games," Theoretical Economics, Econometric Society, vol. 18(4), November.
  • Handle: RePEc:the:publsh:5351
    as

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    References listed on IDEAS

    as
    1. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    2. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 209-244.
    3. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    4. Joyee Deb & Takuo Sugaya & Alexander Wolitzky, 2020. "The Folk Theorem in Repeated Games With Anonymous Random Matching," Econometrica, Econometric Society, vol. 88(3), pages 917-964, May.
    5. Yuichi Yamamoto, 2014. "Individual Learning and Cooperation in Noisy Repeated Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 473-500.
    6. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
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    11. Takuo Sugaya & Alexander Wolitzky, 2021. "Communication and Community Enforcement," Journal of Political Economy, University of Chicago Press, vol. 129(9), pages 2595-2628.
    12. Miguel, Edward & Gugerty, Mary Kay, 2005. "Ethnic diversity, social sanctions, and public goods in Kenya," Journal of Public Economics, Elsevier, vol. 89(11-12), pages 2325-2368, December.
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    More about this item

    Keywords

    Repeated games; symmetric games; incomplete information; commitment types; large populations; population dominant action;
    All these keywords.

    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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