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Time Average Replicator and Best-Reply Dynamics

Department of Mathematics, University of Vienna, A-1090 Vienna, Austria
Equipe Combinatoire et Optimisation, CNRS FRE3232 Faculté de Mathématiques, UPMC-Paris 6, 75013 Paris, France, and Laboratoire d'Econométrie, Ecole Polytechnique, 75005 Paris, France
Ceremade, Université Paris-Dauphine, F-75016 Paris, France
josef.hofbauer{at}univie.ac.at
sorin{at}math.jussieu.fr
viossat{at}ceremade.dauphine.fr

Using an explicit representation in terms of the logit map, we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best-reply dynamics.

Key Words: replicator dynamics; best-reply dynamics; logit map; perturbed differential inclusion; internally chain transitive set; attractor
History: Received: June 30, 2007; revision received: July 10, 2008;