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 suffcient 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
file. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number
bgse38_2005.
Length: 31 Date of creation: Dec 2005 Date of revision: Handle: RePEc:bon:bonedp:bgse38_2005
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany Fax: +49 228 73 9221 Web page: http://www.bgse.uni-bonn.de/index.php?id=494
For technical questions regarding this item, or to correct its listing, contact: (Daniel Park).
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.:
Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2004.
"What to Maximize if You Must,"
Discussion Papers
1414, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
Sergiu Hart & Andreu Mas-Colell, 2001.
"Regret-Based Continuous-Time Dynamics,"
Discussion Paper Series
dp309, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem, revised Apr 2003.
[Downloadable!]
Other versions:
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.)