eprintid: 14527
rev_number: 46
eprint_status: archive
userid: 600
dir: disk0/00/01/45/27
datestamp: 2009-07-29 15:21:32
lastmod: 2024-05-17 12:45:34
status_changed: 2009-07-29 15:21:32
type: working_paper
metadata_visibility: show
creators_name: Hofbauer, J.
creators_name: Oechssler, J.
creators_name: Riedel, F.
creators_id: JHOFB46
creators_id: 
creators_id: 
title: Brown-von Neumann-Nash dynamics: the continuous strategy case
ispublished: pub
subjects: 13200
subjects: 10700
divisions: F59
keywords: JEL classification: C70, 72. Learning in games, evolutionary stability, BNN
note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
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: 2007
publisher: ESRC Centre for Economic Learning and Social Evolution
official_url: https://dx.doi.org/10.2139/ssrn.1015225
vfaculties: VMPS
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
lyricists_name: Hofbauer, J
lyricists_id: JHOFB46
full_text_status: public
series: ELSE Working Papers
number: 203
place_of_pub: London, UK
citation:        Hofbauer, J.;    Oechssler, J.;    Riedel, F.;      (2007)    Brown-von Neumann-Nash dynamics: the continuous strategy case.                    (ELSE Working Papers  203). ESRC Centre for Economic Learning and Social Evolution: London, UK.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/14527/8/Hofbauer_SSRN-id1015225.pdf