IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v74y2012i1p243-256.html
   My bibliography  Save this article

Stochastic games with information lag

Author

Listed:
  • Levy, Yehuda

Abstract

Two-player zero-sum stochastic games with finite state and action spaces are known to have undiscounted values. We study such games under the assumption that one or both players observe the actions of their opponent after some time-dependent delay. We develop criteria for the rate of growth of the delay such that a player subject to such an information lag can still guarantee himself in the undiscounted game as much as he could have with perfect monitoring. We also demonstrate that the player in the Big Match with the absorbing action subject to information lags that grows too rapidly will not be able to guarantee as much as he could have in the game with perfect monitoring.

Suggested Citation

  • Levy, Yehuda, 2012. "Stochastic games with information lag," Games and Economic Behavior, Elsevier, vol. 74(1), pages 243-256.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:243-256
    DOI: 10.1016/j.geb.2011.05.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825611000972
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2011.05.011?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. Truman Bewley & Elon Kohlberg, 1978. "On Stochastic Games with Stationary Optimal Strategies," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 104-125, 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. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    4. C. J. Himmelberg & T. Parthasarathy & F. S. VanVleck, 1976. "Optimal Plans for Dynamic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 390-394, November.
    5. J-M Coulomb, 2003. "Stochastic games without perfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 73-96, December.
    6. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Abraham Neyman, 2001. "Real Algebraic Tools in Stochastic Games," Discussion Paper Series dp272, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Lagziel, David & Lehrer, Ehud, 2015. "Approachability with delayed information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 425-444.
    3. 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.

    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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
    3. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    4. Jean-Francois Mertens & Abraham Neyman & Dinah Rosenberg, 2007. "Absorbing Games with Compact Action Spaces," Discussion Paper Series dp456, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    6. repec:dau:papers:123456789/10880 is not listed on IDEAS
    7. 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.
    8. 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.
    9. 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.
    10. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    11. 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.
    12. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. Laraki, Rida & Renault, Jérôme, 2017. "Acyclic Gambling Games," TSE Working Papers 17-768, Toulouse School of Economics (TSE).
    14. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    15. Bruno Ziliotto, 2016. "General limit value in zero-sum stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 353-374, March.
    16. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    17. Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.
    18. Hansen, Kristoffer Arnsfelt & Ibsen-Jensen, Rasmus & Neyman, Abraham, 2021. "Absorbing games with a clock and two bits of memory," Games and Economic Behavior, Elsevier, vol. 128(C), pages 213-230.
    19. Miquel Oliu-Barton, 2014. "The Asymptotic Value in Finite Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 712-721, August.
    20. 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.
    21. Johannes Horner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2009. "Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem," Cowles Foundation Discussion Papers 1742, Cowles Foundation for Research in Economics, Yale University, revised Aug 2010.

    More about this item

    Keywords

    Stochastic game; Information lag; Incomplete information; Undiscounted value;
    All these keywords.

    JEL classification:

    • 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:eee:gamebe:v:74:y:2012:i:1:p:243-256. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.