On the global convergence of stochastic fictitious play

• 成果类型: Article
• 署名作者: Hofbauer, J; Sandholm, WH
• 署名单位: University of Vienna; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2002.00440.x
• 发表日期: 2002
• 页码: 2265-2294
• 关键词: Nash equilibrium; long-run; games; DYNAMICS; systems; points

摘要

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.