This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

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

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Josef Hofbauer (Dept. of Mathematics, University College London)
Joerg Oechssler (Dept. of Economics, University of Heidelberg)
Frank Riedel (Dept. of Economics, University of Bonn)

Additional information is available for the following registered author(s):

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://129.3.20.41/eps/game/papers/0512/0512003.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0512003.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 31 pages
Date of creation: 15 Dec 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0512003

Note: Type of Document - pdf; pages: 31
Contact details of provider:
Web page: http://129.3.20.41

For technical questions regarding this item, or to correct its listing, contact: (EconWPA).

Related research
Keywords: Learning in games; evolutionary stability; BNN;

Other versions of this item:

Find related papers by 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

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!]
    Other versions:
  2. Ely, Jeffrey C. & Yilankaya, Okan, 2001. "Nash Equilibrium and the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 255-272, April. [Downloadable!] (restricted)
    Other versions:
  3. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July. [Downloadable!] (restricted)
    Other versions:
  4. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December. [Downloadable!] (restricted)
    Other versions:
  5. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March. [Downloadable!] (restricted)
  6. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January. [Downloadable!] (restricted)
    Other versions:
  7. Ross Cressman & Josef Hofbauer & Frank Riedel, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers bgse12_2005, University of Bonn, Germany. [Downloadable!]
  8. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    Other versions:
  9. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November. [Downloadable!] (restricted)
    Other versions:
  10. Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2002. "What to Maximize If You Must," Department of Economics, Working Paper Series 1052, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  11. J. Oechssler & F. Riedel, . "Evolutionary Dynamics on Infinite Strategy Spaces," Sonderforschungsbereich 373 1998-68, Humboldt Universitaet Berlin.
    Other versions:
  12. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July. [Downloadable!] (restricted)
    Other versions:
  13. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Josef Hofbauer & Jörg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Bonn Econ Discussion Papers bgse38_2005, University of Bonn, Germany. [Downloadable!]
    Other versions:
  2. Viossat, Yannick, 2006. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Working Paper Series in Economics and Finance 629, Stockholm School of Economics, revised 21 Jun 2006. [Downloadable!]
  3. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, EconWPA. [Downloadable!]
  4. Gerhard Jäger & Lars Koch-Metzger & Frank Riedel, 2009. "Voronoi languages: Equilibria in cheap-talk games with high-dimensional types and few signals," Working Papers 420, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
  5. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer, vol. 38(2), pages 221-247, June. [Downloadable!] (restricted)
Statistics
Access and download statistics

Did you know? There are NEP reports in over 80 fields that deliver new research to your email.

This page was last updated on 2009-11-5.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.