IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v11y2021i2d10.1007_s13235-020-00364-x.html
   My bibliography  Save this article

Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information

Author

Listed:
  • Dhruva Kartik

    (University of Southern California)

  • Ashutosh Nayyar

    (University of Southern California)

Abstract

A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player’s information at each time can be divided into a common information part and a private information part. Under certain conditions on the evolution of the common and private information, a dynamic programming characterization of the value of the game (if it exists) is presented. If the value of the zero-sum game does not exist, then the dynamic program provides bounds on the upper and lower values of the game.

Suggested Citation

  • Dhruva Kartik & Ashutosh Nayyar, 2021. "Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 11(2), pages 363-388, June.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:2:d:10.1007_s13235-020-00364-x
    DOI: 10.1007/s13235-020-00364-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-020-00364-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-020-00364-x?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. O. G. Haywood, 1954. "Military Decision and Game Theory," Operations Research, INFORMS, vol. 2(4), pages 365-385, November.
    2. 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.
    3. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," HEC Research Papers Series 754, HEC Paris.
    4. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
    5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    6. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
    7. 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.
    8. Jean-Pierre Ponssard & Sylvain Sorin, 1980. "The L-P formulation of finite zero sum games with incomplete information," Post-Print hal-00364266, HAL.
    9. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    10. Dinah Rosenberg, 1998. "Duality and markovian strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 577-597.
    11. Nicky J. Welton & Howard H. Z. Thom, 2015. "Value of Information," Medical Decision Making, , vol. 35(5), pages 564-566, July.
    12. Jérôme Renault, 2012. "The Value of Repeated Games with an Informed Controller," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 154-179, February.
    13. 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.
    14. 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.
    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. Rahul Chandan & Keith Paarporn & Mahnoosh Alizadeh & Jason R. Marden, 2022. "Strategic investments in multi-stage General Lotto games," Papers 2209.06090, arXiv.org.

    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. Bruno Ziliotto, 2016. "A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1522-1534, November.
    2. Ashkenazi-Golan, Galit & Rainer, Catherine & Solan, Eilon, 2020. "Solving two-state Markov games with incomplete information on one side," Games and Economic Behavior, Elsevier, vol. 122(C), pages 83-104.
    3. Jérôme Renault & Xavier Venel, 2017. "Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 349-376, May.
    4. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    5. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    7. Dmitry Khlopin, 2018. "Tauberian Theorem for Value Functions," Dynamic Games and Applications, Springer, vol. 8(2), pages 401-422, June.
    8. 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.
    9. Ziliotto, Bruno, 2018. "Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 486-503.
    10. Rida Laraki & Jérôme Renault, 2020. "Acyclic Gambling Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1237-1257, November.
    11. repec:dau:papers:123456789/10880 is not listed on IDEAS
    12. 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.
    13. Fabien Gensbittel, 2019. "Continuous-Time Markov Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 671-699, September.
    14. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
    15. Guillaume Vigeral, 2013. "A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value," Dynamic Games and Applications, Springer, vol. 3(2), pages 172-186, June.
    16. Dengwang Tang & Hamidreza Tavafoghi & Vijay Subramanian & Ashutosh Nayyar & Demosthenis Teneketzis, 2023. "Dynamic Games Among Teams with Delayed Intra-Team Information Sharing," Dynamic Games and Applications, Springer, vol. 13(1), pages 353-411, March.
    17. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    18. Galit Ashkenazi-Golan & Pen'elope Hern'andez & Zvika Neeman & Eilon Solan, 2022. "Markovian Persuasion with Two States," Papers 2209.06536, arXiv.org.
    19. Hugo Gimbert & Jérôme Renault & Sylvain Sorin & Xavier Venel & Wieslaw Zielonka, 2016. "On the values of repeated games with signals," PSE-Ecole d'économie de Paris (Postprint) hal-01006951, HAL.
    20. Arieli, Itai, 2017. "Payoff externalities and social learning," Games and Economic Behavior, Elsevier, vol. 104(C), pages 392-410.
    21. 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.

    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:dyngam:v:11:y:2021:i:2:d:10.1007_s13235-020-00364-x. 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.