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arXiv · 2310.05741

Fictitious Play for Mean Field Games with Optimal Stopping: Convergence and Computation

Yifan Luo·Chengfeng Shen·Jiajun Tong·Zhennan Zhou
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Abstract

This paper studies mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions. Such a model features a coupled obstacle problem and Fokker-Planck equation posing challenges on top of classic mean field games. The nonconvex nature of exit decisions renders the existence of a classic pure strategy equilibrium infeasible, necessitating the consideration of more complex mixed strategy equilibria. 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. Numerical experiments demonstrate the effectiveness of the proposed method in robustly and efficiently computing mixed equilibria for OSMFGs.

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Yifan Luo, Chengfeng Shen, Jiajun Tong, Zhennan Zhou. 2023-10-09. Fictitious Play for Mean Field Games with Optimal Stopping: Convergence and Computation. https://arxiv.org/abs/2310.05741

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