IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v3y2013i2p279-312.html
   My bibliography  Save this article

Continuous-Time Stochastic Games of Fixed Duration

Author

Listed:
  • Yehuda Levy

    ()

Abstract

We study nonzero-sum continuous-time stochastic games, also known as continuous-time Markov games, of fixed duration. We concentrate on Markovian strategies. We show by way of example that equilibria need not exist in Markovian strategies, but they always exist in Markovian public-signal correlated strategies. To do so, we develop criteria for a strategy profile to be an equilibrium via differential inclusions, both directly and also by modeling continuous-time stochastic as differential games and using the Hamilton–Jacobi–Bellman equations. We also give an interpretation of equilibria in mixed strategies in continuous time and show that approximate equilibria always exist. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
  • Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:279-312
    DOI: 10.1007/s13235-012-0067-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-012-0067-2
    Download Restriction: Access to full text is restricted to subscribers.

    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. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, March.
    2. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    3. repec:eee:gamebe:v:104:y:2017:i:c:p:92-130 is not listed on IDEAS
    4. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    5. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    6. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
    7. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
    8. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    9. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, 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. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
    2. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.
    3. repec:eee:gamebe:v:104:y:2017:i:c:p:92-130 is not listed on IDEAS
    4. Yurii Averboukh, 2017. "Extremal Shift Rule for Continuous-Time Zero-Sum Markov Games," Dynamic Games and Applications, Springer, vol. 7(1), pages 1-20, March.
    5. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.

    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:3:y:2013:i:2:p:279-312. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

    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.