Hofbauer, Josef () (Department of Mathematics, University College London) Oechssler, Jörg () (Department of Economics, University of Heidelberg) Riedel, Frank () (Wirtschaftswissenschaftlicher Fachbereich, Universität Bonn)
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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.
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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number
05-41.
Length: 31 pages Date of creation: 14 Dec 2005 Date of revision: Handle: RePEc:xrs:sfbmaa:05-41
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged. Contact details of provider: Postal: D-68131 Mannheim Phone: (49) (0) 621-292-2547 Fax: (49) (0) 621-292-5594 Email: Web page: http://www.sfb504.uni-mannheim.de/ More information through EDIRC
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!]
HEIFETZ, Aviad & SHANNON, Chris & SPIEGEL, Yossi, 2003.
"What to maximize if you must,"
CORE Discussion Papers
2003047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
[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!]
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