Brown-von Neumann-Nash dynamics : the continuous strategy case


Hofbauer, Josef ; Oechssler, Jörg ; Riedel, Frank


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URL: https://ub-madoc.bib.uni-mannheim.de/2621
URN: urn:nbn:de:bsz:180-madoc-26217
Document Type: Working paper
Year of publication: 2005
Publication language: English
Institution: School of Law and Economics > Sonstige - Fakultät für Rechtswissenschaft und Volkswirtschaftslehre
MADOC publication series: Sonderforschungsbereich 504 > Rationalitätskonzepte, Entscheidungsverhalten und ökonomische Modellierung (Laufzeit 1997 - 2008)
Subject: 300 Social sciences, sociology, anthropology
Classification: JEL: C72 C70,
Subject headings (SWD): Lernen , Nichtkooperatives Spiel , Theorie
Keywords (English): learning in games , evolutionary stability , BNN
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.
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Hofbauer, Josef ; Oechssler, Jörg ; Riedel, Frank (2005) Brown-von Neumann-Nash dynamics : the continuous strategy case. Open Access [Working paper]
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