IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v121y2004i1d10.1023_bjota.0000026133.56615.cf.html
   My bibliography  Save this article

Zero-Sum Stochastic Games with Partial Information

Author

Listed:
  • M. K. Ghosh

    (Indian Institute of Science)

  • D. McDonald

    (University of Ottawa)

  • S. Sinha

    (Jadavpur University)

Abstract

We study a zero-sum stochastic game on a Borel state space where the state of the game is not known to the players. Both players take their decisions based on an observation process. We transform this into an equivalent problem with complete information. Then, we establish the existence of a value and optimal strategies for both players.

Suggested Citation

  • M. K. Ghosh & D. McDonald & S. Sinha, 2004. "Zero-Sum Stochastic Games with Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 99-118, April.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026133.56615.cf
    DOI: 10.1023/B:JOTA.0000026133.56615.cf
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTA.0000026133.56615.cf
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOTA.0000026133.56615.cf?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sylvain Sorin & Shmuel Zamir, 1985. "A 2-Person Game with Lack of Information on 1½ Sides," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 17-23, February.
    2. SORIN, Sylvain, 1984. "'Big match' with lack of information on one side (part 1)," LIDAM Reprints CORE 601, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Dinah Rosenberg & Nicolas Vieille, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 23-35, February.
    4. repec:dau:papers:123456789/6231 is not listed on IDEAS
    5. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
    6. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154, Elsevier.
    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. Subhamay Saha, 2014. "Zero-Sum Stochastic Games with Partial Information and Average Payoff," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 344-354, January.
    2. Yanling Chang & Alan Erera & Chelsea White, 2015. "A leader–follower partially observed, multiobjective Markov game," Annals of Operations Research, Springer, vol. 235(1), pages 103-128, December.

    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. Vieille, Nicolas, 2002. "Stochastic games: Recent results," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 48, pages 1833-1850, Elsevier.
    2. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," HEC Research Papers Series 754, HEC Paris.
    3. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    4. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302553, HAL.
    5. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    6. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," PSE-Ecole d'économie de Paris (Postprint) hal-01302553, HAL.
    7. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Post-Print hal-01302553, HAL.
    8. Jérôme Renault, 2012. "The Value of Repeated Games with an Informed Controller," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 154-179, February.
    9. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
    10. Jérôme Renault, 2006. "The Value of Markov Chain Games with Lack of Information on One Side," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 490-512, August.
    11. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    12. Itai Arieli & Yehuda Levy, 2011. "Infinite sequential games with perfect but incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 207-213, May.
    13. Eilon Solan & Nicolas Vieille, 2000. "Uniform Value in Recursive Games," Discussion Papers 1293, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. 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.
    15. Robert J. Aumann, 2007. "War and Peace," Chapters, in: Jean-Philippe Touffut (ed.), Augustin Cournot: Modelling Economics, chapter 5, Edward Elgar Publishing.
    16. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    17. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. Jacquemet, Nicolas & Koessler, Frédéric, 2013. "Using or hiding private information? An experimental study of zero-sum repeated games with incomplete information," Games and Economic Behavior, Elsevier, vol. 78(C), pages 103-120.
    19. Carmona, G. & Sabourian, H., 2021. "Approachability with Discounting," Cambridge Working Papers in Economics 2124, Faculty of Economics, University of Cambridge.
    20. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.

    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:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026133.56615.cf. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.