IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v46y2017i1d10.1007_s00182-016-0532-z.html
   My bibliography  Save this article

A nested family of $$\varvec{k}$$ k -total effective rewards for positional games

Author

Listed:
  • Endre Boros

    (Rutgers University)

  • Khaled Elbassioni

    () (Masdar Institute of Science and Technology)

  • Vladimir Gurvich

    (Rutgers University
    National Research University, Higher School of Economics)

  • Kazuhisa Makino

    (Research Institute for Mathematical Sciences (RIMS) Kyoto University)

Abstract

Abstract We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each $$k \in \mathbb {N}=\{0,1,\ldots \}$$ k ∈ N = { 0 , 1 , … } we introduce an effective reward function, called k-total. For $$k = 0$$ k = 0 and 1 this function is known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case. For all k, we prove the existence of a saddle point which can be realized by uniformly optimal pure stationary strategies. We also demonstrate that k-total reward games can be embedded into $$(k+1)$$ ( k + 1 ) -total reward games.

Suggested Citation

  • Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino, 2017. "A nested family of $$\varvec{k}$$ k -total effective rewards for positional games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 263-293, March.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0532-z
    DOI: 10.1007/s00182-016-0532-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-016-0532-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    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. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino, 2013. "On Canonical Forms for Zero-Sum Stochastic Mean Payoff Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 128-161, June.
    2. N. N. Pisaruk, 1999. "Mean Cost Cyclical Games," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 817-828, November.
    Full references (including those not matched with items on IDEAS)

    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:46:y:2017:i:1:d:10.1007_s00182-016-0532-z. 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.