IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v65y2007i1p141-152.html
   My bibliography  Save this article

On the existence of almost-pure-strategy Nash equilibrium in n-person finite games

Author

Listed:
  • Wojciech Połowczuk
  • Piotr Więcek
  • Tadeusz Radzik

Abstract

This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous concave (convex) games with compact convex spaces of players’ pure strategies. Copyright Springer-Verlag 2007

Suggested Citation

  • Wojciech Połowczuk & Piotr Więcek & Tadeusz Radzik, 2007. "On the existence of almost-pure-strategy Nash equilibrium in n-person finite games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 141-152, February.
  • Handle: RePEc:spr:mathme:v:65:y:2007:i:1:p:141-152
    DOI: 10.1007/s00186-006-0105-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0105-1
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00186-006-0105-1?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. Radzik, Tadeusz, 1993. "Nash Equilibria of Discontinuous Non-Zero-Sum Two-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 429-437.
    2. Gomez, E, 1988. "Games with Convex Payoff Function in the First Variable," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(3), pages 201-204.
    3. Radzik, Tadeusz, 1991. "Saddle Point Theorems," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 23-32.
    4. Tadeusz Radzik, 2000. "Characterization of optimal strategies in matrix games with convexity properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 211-227.
    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. Tadeusz Radzik, 2014. "Poor convexity and Nash equilibria in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 169-192, February.

    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. Tadeusz Radzik, 2014. "Poor convexity and Nash equilibria in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 169-192, February.
    2. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    3. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    4. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    5. Luciano Méndez-Naya, 2001. "On the Value of Some Infinite Matrix Games," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 82-88, February.
    6. Ismail, M.S., 2014. "A sufficient condition on the existence of pure equilibrium in two-person symmetric zerosum games," Research Memorandum 035, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.

    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:mathme:v:65:y:2007:i:1:p:141-152. 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.