The emergence of rational behavior in the presence of stochastic perturbations
type: Item
instance of: scholarly article
title: The emergence of rational behavior in the presence of stochastic perturbations
zbMATH Open document ID: 1195.91011
DOI: 10.1214/09-AAP651
author: Panayotis Mertikopoulos
author: Aris L. Moustakas
published in: The Annals of Applied Probability
publication date: 2010-09-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/0906.2094
review text: The authors study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. In the presence of stochastic perturbations, this scheme leads to a new stochastic version of the replicator dynamics. The replicator equation obtained is different from the ``aggregate shocks'' approach of evolutionary game theory and it exhibits markedly different rationality properties as well. Irrespective of the perturbations' magnitude, only rationally admissible strategies can survive in the long run. As a result, the game's strict Nash equilibria are stochastically asymptotically stable. The results obtained are illustrated in the case of congestion games.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 91A26
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 5776891
zbMATH Keywords: asymptotic stochastic stability
zbMATH Keywords: congestion games
zbMATH Keywords: dominance
zbMATH Keywords: exponential learning
zbMATH Keywords: Lyapunov function
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: replicator dinamics
zbMATH Keywords: stochastic differential equation
Wikidata QID: Q60142090
MaRDI profile type: Publication
arXiv ID: 0906.2094
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OpenAlex ID: W2000033387
description: scientific article