IDEAS home Printed from https://ideas.repec.org/a/the/publsh/3068.html
   My bibliography  Save this article

Stochastic games with hidden states

Author

Listed:
  • Yamamoto, Yuichi

    (University of Pennsylvania, Department of Economics)

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 uses the idea of random blocks to design an effective punishment mechanism.

Suggested Citation

  • Yamamoto, Yuichi, 2019. "Stochastic games with hidden states," Theoretical Economics, Econometric Society, vol. 14(3), July.
    • Handle: RePEc:the:publsh:3068
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20191115/24497/721
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Kyle Bagwell & Robert Staiger, 1997. "Collusion Over the Business Cycle," RAND Journal of Economics, The RAND Corporation, vol. 28(1), pages 82-106, Spring.
    4. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    5. ,, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    6. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    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. 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.
    10. 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.
    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. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abito, Jose Miguel & Chen, Cuicui, 2023. "A partial identification framework for dynamic games," International Journal of Industrial Organization, Elsevier, vol. 87(C).
    2. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.

    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, Second Version," PIER Working Paper Archive 15-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jun 2015.
    2. 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.
    3. 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.
    4. 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.
    5. Bar-Isaac, Heski & Shapiro, Joel, 2013. "Ratings quality over the business cycle," Journal of Financial Economics, Elsevier, vol. 108(1), pages 62-78.
    6. Chaim Fershtman & Ariel Pakes, 2000. "A Dynamic Oligopoly with Collusion and Price Wars," RAND Journal of Economics, The RAND Corporation, vol. 31(2), pages 207-236, Summer.
    7. Pedro Dal Bó, 2007. "Tacit collusion under interest rate fluctuations," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 533-540, June.
    8. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    9. Fabra, Natalia, 2006. "Collusion with capacity constraints over the business cycle," International Journal of Industrial Organization, Elsevier, vol. 24(1), pages 69-81, January.
    10. Eriksson, Rickard, 2001. "Price Responses to Seasonal Demand Changes in the Swedish Gasoline Market," SSE/EFI Working Paper Series in Economics and Finance 473, Stockholm School of Economics, revised 20 Dec 2001.
    11. Dan Bernhardt & Mahdi Rastad, 2016. "Collusion Under Risk Aversion and Fixed Costs," Journal of Industrial Economics, Wiley Blackwell, vol. 64(4), pages 808-834, December.
    12. Hassan Afrouzi, 2016. "Endogenous firm competition and the cyclicality of markups," Globalization Institute Working Papers 265, Federal Reserve Bank of Dallas.
    13. 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.
    14. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    15. Asplund, Marcus & Eriksson, Rickard & Strand, Niklas, 2001. "Prices, Margins and Liquidity Constraints: Swedish Newspapers 1990-1996," SSE/EFI Working Paper Series in Economics and Finance 470, Stockholm School of Economics.
    16. Neubecker, Leslie, 2002. "Aktienkursorientierte Management-Entlohnung bei korrelierter Entwicklung der Marktnachfrage," Tübinger Diskussionsbeiträge 235, University of Tübingen, School of Business and Economics.
    17. Andrew Kloosterman, 2020. "Cooperation in stochastic games: a prisoner’s dilemma experiment," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 447-467, June.
    18. João Correia-da-Silva & Joana Pinho & Hélder Vasconcelos, 2014. "Sustaining collusion in markets with a general evolution of demand," FEP Working Papers 537, Universidade do Porto, Faculdade de Economia do Porto.
    19. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.
    20. 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.

    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:the:publsh:3068. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.