IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v79y2011i4p1277-1318.html
   My bibliography  Save this article

Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem

Author

Listed:
  • Johannes Hörner
  • Takuo Sugaya
  • Satoru Takahashi
  • Nicolas Vieille

Abstract

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
  • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:4:p:1277-1318
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. 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.
    2. Johannes H�rner & Satoru Takahashi & Nicolas Vieille, 2012. "On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games," Working Papers 1397, Princeton University, Department of Economics, Econometric Research Program..
    3. Wiseman, Thomas & Peski, Marcin, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    4. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
    5. Mitsuhiro Nakamura & Hisashi Ohtsuki, 2016. "Optimal Decision Rules in Repeated Games Where Players Infer an Opponent’s Mind via Simplified Belief Calculation," Games, MDPI, Open Access Journal, vol. 7(3), pages 1-23, July.
    6. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2013. "Dynamic sender–receiver games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 502-534.
    7. Staudigl, Mathias, 2014. "A limit theorem for Markov decision processes," Center for Mathematical Economics Working Papers 475, Center for Mathematical Economics, Bielefeld University.
    8. Barron, Daniel, 2017. "Attaining efficiency with imperfect public monitoring and one-sided Markov adverse selection," Theoretical Economics, Econometric Society, vol. 12(3), September.
    9. Du, Chuang, 2012. "Solving payoff sets of perfect public equilibria: an example," MPRA Paper 38622, University Library of Munich, Germany.
    10. Sebastian Kranz, 2013. "Relational Contracting, Repeated Negotiations, and Hold-Up," Levine's Working Paper Archive 786969000000000676, David K. Levine.
    11. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    12. 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.
    13. Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    14. Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Levine's Working Paper Archive 786969000000000423, David K. Levine.
    15. 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.
    16. Richter, Michael, 2014. "Fully absorbing dynamic compromise," Journal of Economic Theory, Elsevier, vol. 152(C), pages 92-104.
    17. 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.
    18. John Duggan, 2013. "A Folk Theorem for Repeated Elections with Adverse Selection," Wallis Working Papers WP64, University of Rochester - Wallis Institute of Political Economy.
    19. Guéron, Yves, 2015. "Failure of gradualism under imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 128-145.

    More about this item

    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:ecm:emetrp:v:79:y:2011:i:4:p:1277-1318. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/essssea.html .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.