IDEAS home Printed from https://ideas.repec.org/p/xrs/sfbmaa/05-41.html

Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case

Author

Listed:
  • Hofbauer, Josef

    (Department of Mathematics, University College London)

  • Oechssler, Jörg

    (Department of Economics, University of Heidelberg)

  • Riedel, Frank

    (Wirtschaftswissenschaftlicher Fachbereich, Universität Bonn)

Abstract

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown—von Neumann—Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.

Suggested Citation

  • Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Sonderforschungsbereich 504 Publications 05-41, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    • Handle: RePEc:xrs:sfbmaa:05-41
    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
    as

    Download full text from publisher

    File URL: http://www.sfb504.uni-mannheim.de/publications/dp05-41.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    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:xrs:sfbmaa:05-41. 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: Carsten Schmidt The email address of this maintainer does not seem to be valid anymore. Please ask Carsten Schmidt to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/sfmande.html .

    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.