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

35 Pages Posted: 18 Sep 2007

See all articles by Joerg Oechssler

Joerg Oechssler

University of Heidelberg - Alfred Weber Institute for Economics

Josef Hofbauer

University of Vienna - Department of Mathematics

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Date Written: September 2007

Abstract

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown--von Neumann--Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics, allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained.

Keywords: learning in games, evolutionary stability, BNN

JEL Classification: C70, C72

Suggested Citation

Oechssler, Joerg and Hofbauer, Josef and Riedel, Frank, Brown-Von Neumann-Nash Dynamics: The Continuous Strategy Case (September 2007). Available at SSRN: https://ssrn.com/abstract=1015225 or http://dx.doi.org/10.2139/ssrn.1015225

Joerg Oechssler (Contact Author)

University of Heidelberg - Alfred Weber Institute for Economics ( email )

Grabengasse 14
Heidelberg, D-69117
Germany
+49 6221 54 3548 (Phone)
+49 6221 54 3630 (Fax)

HOME PAGE: http://www.awi.uni-heidelberg.de/with2/theorie2/Team/Oechssler/Oechssler_main.html

Josef Hofbauer

University of Vienna - Department of Mathematics ( email )

Oskar-Morgenstern-Platz 1
A-1090 Vienna
Austria

Frank Riedel

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
61
Abstract Views
799
rank
384,159
PlumX Metrics