Log-linear dynamics and local potential

• 成果类型: Article
• 署名作者: Okada, Daijiro; Tercieux, Olivier
• 署名单位: Paris School of Economics; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.01.011
• 发表日期: 2012
• 页码: 1140-1164
• 关键词: Log-linear dynamic; Relative log-linear dynamic; stochastic stability; Local potential maximizer; equilibrium selection; Stochastic order; Comparison of Markov chains

摘要

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 x 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. (C) 2012 Elsevier Inc. All rights reserved.