IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v109y2001i2d10.1023_a1017530825781.html
   My bibliography  Save this article

A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality

Author

Listed:
  • A. ZIAD

    (Université de Caen)

Abstract

In this paper, a very simple example shows that, in a n- person nonzero-sum game, the quasiconvexity of the payoff functions is not sufficient to establish the 0-diagonal quasiconcavity in the Fan minimax inequality.

Suggested Citation

  • A. Ziad, 2001. "A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 457-462, May.
  • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017530825781
    DOI: 10.1023/A:1017530825781
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1017530825781
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1023/A:1017530825781?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. M. B. Lignola, 1997. "Ky Fan Inequalities and Nash Equilibrium Points without Semicontinuity and Compactness," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 137-145, July.
    2. X. Zhang, 1997. "Some Intersection Theorems and Minimax Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 195-207, July.
    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. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    2. Brânzei, R. & Morgan, J. & Scalzo, V. & Tijs, S.H., 2002. "Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory," Discussion Paper 2002-17, Tilburg University, Center for Economic Research.
    3. C. Pensevalle & G. Pieri, 2000. "On Existence of Nash Equilibria of Games with Constraints on Multistrategies," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 601-613, December.
    4. Rabia Nessah & Kristiaan Kerstens, 2008. "Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets," Working Papers 2008-ECO-13, IESEG School of Management.
    5. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    6. Francesco Ciardiello, 2007. "Some Examples and Counterexamples about Continuity on Equilibrium Problems," Quaderni DSEMS 16-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    7. Francesco Ciardiello, 2007. "Convexity on Nash Equilibria without Linear Structure," Quaderni DSEMS 15-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    8. Tian, Guoqiang, 2012. "A Full Characterization on Fixed-Point Theorem, Minimax Inequality, Saddle Point, and KKM Theorem," MPRA Paper 57929, University Library of Munich, Germany, revised Jul 2014.
    9. Rabia Nessah & Guoqiang Tian, 2008. "Existence of Equilibrium in Minimax Inequalities, Saddle Points, Fixed Points, and Games without Convexity Sets," Working Papers 2008-ECO-15, IESEG School of Management, revised Nov 2010.
    10. Xinyu Zhang & Chunyan Yang & Renjie Han & Shiqing Zhang, 2024. "Nash’s Existence Theorem for Non-Compact Strategy Sets," Mathematics, MDPI, vol. 12(13), pages 1-10, June.

    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:joptap:v:109:y:2001:i:2:d:10.1023_a:1017530825781. 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.