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Title:Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case PDF Logo
Authors:Hofbauer, Josef
Oechssler, Jörg
Riedel, Frank
Issue Date:2005
Series/Report no.:Bonn econ discussion papers 2005,38
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.
Subjects:learning in games
evolutionary stability
BNN
JEL:C70
C72
Document Type:Working Paper
Appears in Collections:Bonn Econ Discussion Papers, Bonn Graduate School of Economics (BGSE), Universität Bonn

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