Log-linear dynamics and local potential

Daijiro Okada and Olivier Tercieux ()
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Daijiro Okada: Department of Economics - RU - Rutgers, The State University of New Jersey [New Brunswick] - Rutgers - Rutgers University System
Olivier Tercieux: PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: We show that local potential maximizer (Morris and Ui (2005) [14]), a generalization of potential maximizer, is stochastically stable in the log-linear dynamic if the payoff functions are, or the associated local potential is, supermodular. Thus an equilibrium selection result similar to those on robustness to incomplete information (Morris and Ui (2005) [14]), and on perfect foresight dynamic (Oyama et al. (2008) [18]) holds for the log-linear dynamic. An example shows that stochastic stability of an LP-max is not guaranteed for non-potential games without the supermodularity condition. We investigate sensitivity of the log-linear dynamic to cardinal payoffs and its consequence on the stability of weighted local potential maximizer. In particular, for 2×2 games, we examine a modified log-linear dynamic (relative log-linear dynamic) under which local potential maximizer with positive weights is stochastically stable. The proof of the main result relies on an elementary method for stochastic ordering of Markov chains.

Keywords: Log-linear dynamic; Relative log-linear dynamic; Stochastic stability; Local potential maximizer; Equilibrium selection; Stochastic order; Comparison of Markov chains (search for similar items in EconPapers)
Date: 2012-05
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Citations: View citations in EconPapers (10)

Published in Journal of Economic Theory, 2012, 147 (3), pp.1140-1164. ⟨10.1016/j.jet.2012.01.011⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-00754591

DOI: 10.1016/j.jet.2012.01.011

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