Template-Type: ReDIF-Paper 1.0
Title: Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case
Author-Name: Josef Hofbauer
Author-Name: Jörg Oechssler
Author-Name: Frank Riedel
Author-Email: frank.riedel@uni-bonn.de
Classification-JEL: C70, C72
Keywords: 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 suffcient conditions for local and global 
	asymptotic stability which use concepts developed in evolutionary game theory.
Note: 
Length: 31
Creation-Date: 2005-12
Revision-Date: 
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse38_2005.pdf
File-Format: application/pdf
Handle: RePEc:bon:bonedp:bgse38_2005