IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v118y2003i3d10.1023_bjota.0000004867.66302.16.html
   My bibliography  Save this article

An Approach to Fuzzy Noncooperative Nash Games

Author

Listed:
  • D. Garagic

    (Ohio State University)

  • J.B. Cruz

    (Ohio State University)

Abstract

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends. In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.

Suggested Citation

  • D. Garagic & J.B. Cruz, 2003. "An Approach to Fuzzy Noncooperative Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 475-491, September.
  • Handle: RePEc:spr:joptap:v:118:y:2003:i:3:d:10.1023_b:jota.0000004867.66302.16
    DOI: 10.1023/B:JOTA.0000004867.66302.16
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTA.0000004867.66302.16
    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/B:JOTA.0000004867.66302.16?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. J. B. Cruz & M. A. Simaan, 2000. "Ordinal Games and Generalized Nash and Stackelberg Solutions," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 205-222, November.
    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. Svajone Bekesiene & Serhii Mashchenko, 2023. "On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies," Mathematics, MDPI, vol. 11(22), pages 1-12, November.
    2. Luigi Di Gaetano & Isidoro Mazza & Anna Mignosa, 2019. "On the allocation of talents in the contemporary art market," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 43(1), pages 121-143, March.

    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. Jamal Ouenniche & Aristotelis Boukouras & Mohammad Rajabi, 2016. "An Ordinal Game Theory Approach to the Analysis and Selection of Partners in Public–Private Partnership Projects," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 314-343, April.
    2. J. M. Peterson & M. A. Simaan, 2008. "Probabilities of Pure Nash Equilibria in Matrix Games when the Payoff Entries of One Player Are Randomly Selected," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 401-410, May.
    3. M. Wei & J. B. Cruz, 2006. "Two Game Models for Cooperation with Implicit Noncooperation," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 505-527, September.
    4. Naouel Yousfi-Halimi & Mohammed Said Radjef & Hachem Slimani, 2018. "Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations," Annals of Operations Research, Springer, vol. 267(1), pages 607-628, August.
    5. Fabian R. Pieroth & Martin Bichler, 2022. "$\alpha$-Rank-Collections: Analyzing Expected Strategic Behavior with Uncertain Utilities," Papers 2211.10317, arXiv.org, revised Aug 2024.
    6. Andrea Collevecchio & Hlafo Alfie Mimun & Matteo Quattropani & Marco Scarsini, 2024. "Basins of Attraction in Two-Player Random Ordinal Potential Games," Papers 2407.05460, arXiv.org.

    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:118:y:2003:i:3:d:10.1023_b:jota.0000004867.66302.16. 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.