IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v27y1998i3p393-405.html
   My bibliography  Save this article

Paths leading to the Nash set for nonsmooth games

Author

Listed:
  • Yakar Kannai

    (Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel 76100)

  • (*), Emmanuel Tannenbaum

    (Department of Chemical Engineering and Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA)

Abstract

Maschler, Owen and Peleg (1988) constructed a dynamic system for modelling a possible negotiation process for players facing a smooth n-person pure bargaining game, and showed that all paths of this system lead to the Nash point. They also considered the non-convex case, and found in this case that the limiting points of solutions of the dynamic system belong to the Nash set. Here we extend the model to i) general convex pure bargaining games, and to ii) games generated by "divide the cake" problems. In each of these cases we construct a dynamic system consisting of a differential inclusion (generalizing the Maschler-Owen-Peleg system of differential equations), prove existence of solutions, and show that the solutions converge to the Nash point (or Nash set). The main technical point is proving existence, as the system is neither convex valued nor continuous. The intuition underlying the dynamics is the same as (in the convex case) or analogous to (in the division game) that of Maschler, Owen, and Peleg.

Suggested Citation

  • Yakar Kannai & (*), Emmanuel Tannenbaum, 1998. "Paths leading to the Nash set for nonsmooth games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 393-405.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:3:p:393-405
    Note: Received August 1997/Final version May 1998
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/8027003/80270393.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kannai, Yakar, 2003. "Costly Nash paths," Games and Economic Behavior, Elsevier, vol. 45(1), pages 171-180, October.
    2. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.

    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:jogath:v:27:y:1998:i:3:p:393-405. 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: 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.