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

Josef Hofbauer, Jörg Oechssler and Frank Riedel ()

Bonn Econ Discussion Papers from University of Bonn, Germany

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 suffcient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.

Keywords: learning in games; evolutionary stability; BNN (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-knm
Date: 2005-12
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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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