IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v7y2017i3d10.1007_s13235-016-0189-z.html
   My bibliography  Save this article

On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps

Author

Listed:
  • Ilaria Brunetti

    (University of Avignon
    INRIA Sophia Antipolis)

  • Vladimir Gaitsgory

    (Macquarie University)

  • Eitan Altman

    (INRIA Sophia Antipolis
    LINCS)

Abstract

We study a nonzero-sum game considered on the solutions of a hybrid dynamical system that evolves in continuous time and that is subjected to abrupt changes in parameters. The changes in the parameters are synchronized with (and determined by) the changes in the states–actions of two Markov decision processes, each of which is controlled by a player who aims at minimizing his or her objective function. The lengths of the time intervals between the “jumps” of the parameters are assumed to be small. We show that an asymptotic Nash equilibrium of such hybrid game can be constructed on the basis of a Nash equilibrium of a deterministic averaged dynamic game.

Suggested Citation

  • Ilaria Brunetti & Vladimir Gaitsgory & Eitan Altman, 2017. "On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps," Dynamic Games and Applications, Springer, vol. 7(3), pages 386-401, September.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0189-z
    DOI: 10.1007/s13235-016-0189-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-016-0189-z
    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/s13235-016-0189-z?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. Peng Shi & Eitan Altman & Vladimir Gaitsgory, 1998. "On asymptotic optimization of a class of nonlinear stochastic hybrid systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 289-315, June.
    Full references (including those not matched with items on IDEAS)

    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. G. Badowski & G. Yin & Q. Zhang, 2003. "Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 131-166, January.
    2. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.

    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:7:y:2017:i:3:d:10.1007_s13235-016-0189-z. 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.