IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v37y2008i4p581-596.html
   My bibliography  Save this article

Existence of optimal strategies in Markov games with incomplete information

Author

Abstract

The existence of a value and optimal strategies is proved for the class of twoperson repeated games where the state follows a Markov chain independently of players’ actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard signaling where players’ stage actions are observable, as well as to the model with general signals provided that player one has a nonrevealing repeated game strategy. The proofs reduce the analysis of these repeated games to that of classical repeated games with incomplete information on one side.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Abraham Neyman, 2008. "Existence of optimal strategies in Markov games with incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 581-596, December.
    • Handle: RePEc:spr:jogath:v:37:y:2008:i:4:p:581-596
    DOI: 10.1007/s00182-008-0134-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-008-0134-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-008-0134-5?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    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. Fabien Gensbittel, 2019. "Continuous-Time Markov Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 671-699, September.
    2. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Xavier Bressaud & Anthony Quas, 2017. "Dynamical Analysis of a Repeated Game with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1085-1105, November.
    4. Johannes Hörner & Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2010. "On a Markov Game with One-Sided Information," Operations Research, INFORMS, vol. 58(4-part-2), pages 1107-1115, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    10. Johannes Horner & Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2009. "On a Markov Game with One-Sided Incomplete Information," Cowles Foundation Discussion Papers 1737, Cowles Foundation for Research in Economics, Yale University.
    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. 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. 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.
    14. 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.

    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. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "The MaxMin value of stochastic games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 133-150, December.
    3. Xiaochi Wu, 2022. "Existence of value for a differential game with asymmetric information and signal revealing," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 213-247, March.
    4. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    5. Andrew Kosenko, 2020. "Mediated Persuasion," Papers 2012.00098, arXiv.org, revised Dec 2020.
    6. Xiaochi Wu, 2021. "Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case," Dynamic Games and Applications, Springer, vol. 11(4), pages 863-891, December.
    7. Vida, Péter & Āzacis, Helmuts, 2013. "A detail-free mediator," Games and Economic Behavior, Elsevier, vol. 81(C), pages 101-115.
    8. Frédéric Koessler & Françoise Forges, 2008. "Multistage Communication With And Without Verifiable Types," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 145-164.
    9. Marie Laclau & Tristan Tomala, 2016. "Repeated games with public information revisited," PSE Working Papers hal-01285326, HAL.
    10. Makoto Shimoji, 2016. "Rationalizable Persuasion," Discussion Papers 16/08, Department of Economics, University of York.
    11. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    12. Smolin, Alex & Ichihashi, Shota, 2022. "Data Collection by an Informed Seller," TSE Working Papers 22-1330, Toulouse School of Economics (TSE).
    13. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    14. Andreas Haupt & Zoe Hitzig, 2023. "Opaque Contracts," Papers 2301.13404, arXiv.org.
    15. Elliot Lipnowski & Doron Ravid & Denis Shishkin, 2024. "Perfect Bayesian Persuasion," Papers 2402.06765, arXiv.org.
    16. Thomas Mariotti & Nikolaus Schweizer & Nora Szech & Jonas von Wangenheim, 2023. "Information Nudges and Self-Control," Management Science, INFORMS, vol. 69(4), pages 2182-2197, April.
    17. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    18. Golosov, Mikhail & Skreta, Vasiliki & Tsyvinski, Aleh & Wilson, Andrea, 2014. "Dynamic strategic information transmission," Journal of Economic Theory, Elsevier, vol. 151(C), pages 304-341.
    19. 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.
    20. Galit Ashkenazi-Golan & Pen'elope Hern'andez & Zvika Neeman & Eilon Solan, 2022. "Markovian Persuasion with Two States," Papers 2209.06536, arXiv.org.

    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:jogath:v:37:y:2008:i:4:p:581-596. 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.