Monotone imitation dynamics in large populations

• 成果类型: Article
• 署名作者: Fudenberg, Drew; Imhof, Lorens A.
• 署名单位: Harvard University; University of Bonn
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2007.08.002
• 发表日期: 2008
• 页码: 229-245
• 关键词: Equilibrium selection; Learning model; limit distribution; Markov Process; prisoner's dilemma

摘要

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [Muddling through: noisy equilibrium selection, J. Econ. Theory 74 (1997) 235-265] and the related processes proposed by Benaim and Weibull [Deterministic approximation of stochastic evolution in games, Econometrica 71 (2003) 873-903] and Traulsen et al. [Coevolutionary dynamics: from finite to infinite populations, Phys. Rev. Lett. 95 (2005) 238701], as well as the frequency-dependent Moran process studied by Fudenberg et al. [Evolutionary game dynamics in finite populations with strong selection and weak mutation, Theoretical Population Biol. 70 (2006) 352-363]. We illustrate our results by considering the effect of the number of periods of repetition on the selected equilibrium in repeated play of the prisoner's dilemma when players are restricted to a small set of simple strategies. (c) 2007 Elsevier Inc. All rights reserved.