IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v20y2018i04ns021919891850010x.html
   My bibliography  Save this article

The Computational Complexity of Finding a Mixed Berge Equilibrium for a k-Person Noncooperative Game in Normal Form

Author

Listed:
  • Ahmad Nahhas

    (Center on Stochastic Modeling, Optimization, and Statistics (COSMOS), UT Arlington College of Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA)

  • H. W. Corley

    (Center on Stochastic Modeling, Optimization, and Statistics (COSMOS), UT Arlington College of Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA)

Abstract

The mixed Berge equilibrium (MBE) is an extension of the Berge equilibrium (BE) to mixed strategies. The MBE models mutually support in a k-person noncooperative game in normal form. An MBE is a mixed-strategy profile for the k players in which every k − 1 players have mixed strategies that maximize the expected payoff for the remaining player’s equilibrium strategy. In this paper, we study the computational complexity of determining whether an MBE exists in a k-person normal-form game. For a two-person game, an MBE always exists and the problem of finding an MBE is PPAD-complete. In contrast to the mixed Nash equilibrium, the MBE is not guaranteed to exist in games with three or more players. Here we prove, when k ≥ 3, that the decision problem of asking whether an MBE exists for a k-person normal-form game is NP-complete. Therefore, in the worst-case scenario there does not exist a polynomial algorithm that finds an MBE unless P=NP.

Suggested Citation

  • Ahmad Nahhas & H. W. Corley, 2018. "The Computational Complexity of Finding a Mixed Berge Equilibrium for a k-Person Noncooperative Game in Normal Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-13, December.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:04:n:s021919891850010x
    DOI: 10.1142/S021919891850010X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021919891850010X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021919891850010X?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.

    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:wsi:igtrxx:v:20:y:2018:i:04:n:s021919891850010x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.