This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a generalized fictitious play algorithm that computes OSMFG mixed equilibria by iteratively solving pure strategy systems, i.e. approximating mixed strategies through averaging pure strategies according to a certain updating rule. The generalized fictitious play allows for a broad family of learning rates and the convergence to the mixed strategy equilibrium can be rigorously justified. The algorithm also incorporates efficient finite difference schemes of the pure strategy system, and numerical experiments demonstrate the effectiveness of the proposed method in robustly and efficiently computing mixed equilibria for OSMFGs.

翻译：本文研究具有最优停止时间的均值场博弈（OSMFGs），其中博弈方需做出最优退出决策，此类模型中耦合的障碍方程与福克-普朗克方程相较于经典均值场博弈带来了求解挑战。本文提出一种广义虚拟博弈算法，通过对纯策略系统进行迭代求解（即依据特定更新规则对纯策略取平均以近似混合策略），来计算OSMFG的混合均衡。该广义虚拟博弈兼容宽泛的学习率族，且能够严格证明其收敛于混合策略均衡。算法集成了纯策略系统的高效有限差分格式，数值实验证明了所提方法在稳健且高效地计算OSMFG混合均衡方面的有效性。