A behavioral learning process in games

• 成果类型: Article
• 署名作者: Laslier, JF; Topol, R; Walliser, B
• 署名单位: Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); heSam Universite; Conservatoire National Arts & Metiers (CNAM); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1006/game.2000.0841
• 发表日期: 2001
• 页码: 340-366
• 关键词: evolution; learning; Nash equilibrium; Polya urn; reinforcement

摘要

This paper studies the cumulative proportional reinforcement (CPR) rule, according to which an agent plays, at each period, an action with a probability proportional to the cumulative utility that the agent has obtained with that action. The asymptotic properties of this learning process are examined for a decision-maker under risk, where it converges almost surely toward the expected utility maximizing action(s). The process is further considered in a two-player game; it converges with positive probability toward any strict pure Nash equilibrium and converges with zero probability toward some mixed equilibria (which are characterized). The CPR rule is compared in its principles with other reinforcement rules and with replicator dynamics. (C) 2001 Academic Press.