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

Josef Hofbauer, Jörg Oechssler and Frank Riedel ()

No 05-41, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim

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.

Date: 2005-12-14
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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Related works:
Working Paper: Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case (2005)
Working Paper: Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case (2005)
Working Paper: Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case (2005)
Journal Article: Brown-von Neumann-Nash dynamics: The continuous strategy case (2009)
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