IDEAS home Printed from https://ideas.repec.org/p/pen/papers/16-012.html
   My bibliography  Save this paper

Stochastic Games With Hidden States, Fourth Version

Author

Listed:
  • Yuichi Yamamoto

    (Department of Economics, University of Pennsylvania)

Abstract

This paper studies infinite-horizon stochastic games in which players observe payoffs and noisy public information about a hidden state each period.We find that, very generally, the feasible and individually rational payoff set is invariant to the initial prior about the state in the limit as the discount factor goes to one. This result ensures that players can punish or reward the opponents via continuation payoffs in a flexible way. Then we prove the folk theorem, assuming that public randomization is available. The proof is constructive, and introduces the idea of random blocks to design an effective punishment mechanism.

Suggested Citation

  • 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.
    • Handle: RePEc:pen:papers:16-012
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/SSRN%2016_012%20fourth%20version.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    3. John Haltiwanger & Joseph E. Harrington Jr., 1991. "The Impact of Cyclical Demand Movements on Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 22(1), pages 89-106, Spring.
    4. Kyle Bagwell & Robert Staiger, 1997. "Collusion Over the Business Cycle," RAND Journal of Economics, The RAND Corporation, vol. 28(1), pages 82-106, Spring.
    5. 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..
    6. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    7. 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.
    8. Michihiro Kandori, 1991. "Correlated Demand Shocks and Price Wars During Booms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 171-180.
    9. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2000. "Blackwell Optimality in Markov Decision Processes with Partial Observation," Discussion Papers 1292, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. ,, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    11. 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.
    12. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    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. Michihiro Kandori, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 581-593.
    15. 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.
    16. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    17. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, March.
    18. Drew Fudenberg & David K. Levine & Jean Tirole, 1985. "Infinite-Horizon Models of Bargaining with One-Sided Incomplete Information," Levine's Working Paper Archive 1098, David K. Levine.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yuichi Yamamoto, 2014. "Stochastic Games with Hidden States, Second Version," PIER Working Paper Archive 15-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jun 2015.
    3. Yuichi Yamamoto, 2015. "Stochastic Games with Hidden States," PIER Working Paper Archive 15-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Yamamoto, Yuichi, 2019. "Stochastic games with hidden states," Theoretical Economics, Econometric Society, vol. 14(3), July.
    5. 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.
    6. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.
    7. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.
    8. Dou, Winston Wei & Ji, Yan & Wu, Wei, 2021. "Competition, profitability, and discount rates," Journal of Financial Economics, Elsevier, vol. 140(2), pages 582-620.
    9. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2013. "Optimal collusion with limited liability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 203-227, September.
    10. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    11. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Tristan Tomala, 2013. "Belief-Free Communication Equilibria in Repeated Games," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 617-637, November.
    13. Snyder, Christopher M., 1998. "Why do larger buyers pay lower prices? Intense supplier competition," Economics Letters, Elsevier, vol. 58(2), pages 205-209, February.
    14. Joseph E. Harrington, Jr, 2005. "Detecting Cartels," Economics Working Paper Archive 526, The Johns Hopkins University,Department of Economics.
    15. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    16. Pedro Dal Bo, 2002. "Three Essays on Repeated Games," Levine's Working Paper Archive 618897000000000038, David K. Levine.
    17. Juan‐Pablo Montero & Juan Ignacio Guzman, 2010. "Output‐Expanding Collusion In The Presence Of A Competitive Fringe," Journal of Industrial Economics, Wiley Blackwell, vol. 58(1), pages 106-126, March.
    18. Bar-Isaac, Heski & Shapiro, Joel, 2013. "Ratings quality over the business cycle," Journal of Financial Economics, Elsevier, vol. 108(1), pages 62-78.
    19. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    20. 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.

    More about this item

    Keywords

    stochastic game; hidden state; uniform connectedness; robust connectedness; random blocks; folk theorem;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pen:papers:16-012. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.