Stochastic adaptive learning with committed players in games with strict Nash equilibria

• 成果类型: Article
• 署名作者: Funai, Naoki
• 署名单位: Shiga University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2025.09.011
• 发表日期: 2025
• 关键词: evolutionary dynamics; rational cooperation; models; approximation

摘要

We investigate the convergence properties of an adaptive learning model that overlaps those of stochastic fictitious play learning and experience-weighted attraction learning in normal form games with strict Nash equilibria. In particular, we consider the case in which adaptive players play a game against not only other adaptive players but also committed players, who do not revise their behaviour but follow a fixed (strict Nash equilibrium or corresponding logit quantal response equilibrium) action. We then provide conditions under which the adaptive learning process, the choice probability profile of adaptive players, almost surely converges to the logit quantal response equilibrium that committed players follow. We also provide conditions under which the adaptive learning process of a more general adaptive learning model which overlaps those of payoff assessment learning and delta learning converges to a logit quantal response equilibrium different from the equilibrium that committed players follow with positive probability.