On the Global Convergence of Stochastic Fictitious Play
证明随机虚拟博弈在四类博弈（内点ESS、零和、势博弈、超模博弈）中全局收敛，利用随机逼近理论和Lyapunov函数，对研究学习动态的经济学者有参考价值。
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.