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The folk theorem for irreducible stochastic games with imperfect public monitoring

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  • Fudenberg, Drew
  • Yamamoto, Yuichi

Abstract

This paper introduces stochastic games with imperfect public signals. It provides a sufficient condition for the folk theorem when the game is irreducible, thus generalizing the results of Dutta (1995) [5] and Fudenberg, Levine, and Maskin (1994) [9]. To do this, the paper extends the concept of self-generation (Abreu, Pearce, and Stacchetti, 1990 [1]) to "return generation," which explicitly tracks actions and incentives until the next time the state returns to its current value, and asks that players not wish to deviate given the way their continuation payoffs from the time of this return depend on the public signals that have been observed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1664-1683
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414.
    2. Glenn Ellison, 1994. "Theories of Cartel Stability and the Joint Executive Committee," RAND Journal of Economics, The RAND Corporation, vol. 25(1), pages 37-57, Spring.
    3. repec:wsi:wschap:9789812818478_0012 is not listed on IDEAS
    4. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307 World Scientific Publishing Co. Pte. Ltd..
    5. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2010. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Econometrica, Econometric Society, vol. 78(2), pages 453-508, March.
    6. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    7. Dilip Abreu & David Pearce & Ennio Stacchetti, 2010. "Towards a Theory of Discounted Repeated Games with Imperfect Monitoring," Levine's Working Paper Archive 199, David K. Levine.
    8. 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..
    9. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1773-1814.
    10. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    11. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    12. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
    13. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2008. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," GSIA Working Papers 2009-E22, Carnegie Mellon University, Tepper School of Business.
    14. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    15. Prajit K. Dutta, 1997. "A Folk Theorem for Stochastic Games," Levine's Working Paper Archive 1000, David K. Levine.
    16. 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.
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    Citations

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    Cited by:

    1. Seok-ju Cho & John Duggan, 2015. "A folk theorem for the one-dimensional spatial bargaining model," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 933-948, November.
    2. Peski, Marcin & Wiseman, Thomas, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    3. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
    4. Barron, Daniel, 2017. "Attaining efficiency with imperfect public monitoring and one-sided Markov adverse selection," Theoretical Economics, Econometric Society, vol. 12(3), September.
    5. Sebastian Kranz, 2013. "Relational Contracting, Repeated Negotiations, and Hold-Up," Cowles Foundation Discussion Papers 1888, Cowles Foundation for Research in Economics, Yale University.
    6. repec:eee:gamebe:v:103:y:2017:i:c:p:185-198 is not listed on IDEAS
    7. Yuichi Yamamoto, 2014. "Stochastic Games with Hidden States, Fifth version," PIER Working Paper Archive 18-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 19 May 2018.
    8. Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Cowles Foundation Discussion Papers 1847, Cowles Foundation for Research in Economics, Yale University.
    9. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    10. Aislinn Bohren, 2016. "Using Persistence to Generate Incentives in a Dynamic Moral Hazard Problem," PIER Working Paper Archive 16-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 15 Oct 2016.
    11. Yuichi Yamamoto, 2014. "Stochastic Games With Hidden States, Fourth Version," PIER Working Paper Archive 16-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Nov 2017.
    12. Aislinn Bohren, 2018. "Using Persistence to Generate Incentives in a Dynamic Moral Hazard Problem," PIER Working Paper Archive 18-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Apr 2018.
    13. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Journal of Economic Theory, Elsevier, vol. 150(C), pages 487-514.
    14. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    15. Hörner, Johannes & Takahashi, Satoru & Vieille, Nicolas, 2014. "On the limit perfect public equilibrium payoff set in repeated and stochastic games," Games and Economic Behavior, Elsevier, vol. 85(C), pages 70-83.
    16. 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.
    17. Herings P.J.J. & Meshalkin A. & Predtetchinski A., 2012. "A Folk Theorem for Bargaining Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Richter, Michael, 2014. "Fully absorbing dynamic compromise," Journal of Economic Theory, Elsevier, vol. 152(C), pages 92-104.
    19. repec:spr:joecth:v:66:y:2018:i:1:d:10.1007_s00199-017-1060-1 is not listed on IDEAS
    20. Aiba, Katsuhiko, 2014. "A folk theorem for stochastic games with private almost-perfect monitoring," Games and Economic Behavior, Elsevier, vol. 86(C), pages 58-66.
    21. John Duggan, 2013. "A Folk Theorem for Repeated Elections with Adverse Selection," Wallis Working Papers WP64, University of Rochester - Wallis Institute of Political Economy.

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