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We Can Cooperate Even When the Monitoring Structure Will Never Be Known

Author

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  • Yuichi Yamamoto

    () (Department of Economics, University of Pennsylvania)

Abstract

This paper considers infinite-horizon stochastic games with hidden states and hidden actions. The state changes over time, players observe only a noisy public signal about the state each period, and actions are private information. In this model, uncertainty about the monitoring structure does not disappear. We show how to construct an approximately efficient equilibrium in a repeated Cournot game. Then we extend it to a general case and obtain the folk theorem using ex-post equilibria under a mild condition.

Suggested Citation

  • Yuichi Yamamoto, 2014. "We Can Cooperate Even When the Monitoring Structure Will Never Be Known," PIER Working Paper Archive 17-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 08 Apr 2017.
  • Handle: RePEc:pen:papers:17-011
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    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/SSRN%2017_011.pdf
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    References listed on IDEAS

    as
    1. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    3. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    4. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    5. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    6. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    7. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273 World Scientific Publishing Co. Pte. Ltd..
    8. Yuichi Yamamoto, 2014. "Individual Learning and Cooperation in Noisy Repeated Games," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 473-500.
    9. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    10. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    11. Wiseman, Thomas, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    12. repec:dau:papers:123456789/9834 is not listed on IDEAS
    13. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    14. Roy Radner & Roger Myerson & Eric Maskin, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 59-69.
    15. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    16. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
    17. Tristan Tomala & J. Hörner & S. Lovo, 2009. "Existence of belief-free equilibria in games with incomplete information and known-own payoffs," Post-Print hal-00495690, HAL.
    18. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
    19. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    20. Drew Fudenberg & Yuichi Yamamoto, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Econometrica, Econometric Society, vol. 78(5), pages 1673-1710, September.
    21. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    stochastic game; hidden state; public monitoring; pseudoergodic strategy; folk theorem; ex-post equilibrium;

    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

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