Discrete potential mean field games: duality and numerical resolution

• 成果类型: Article
• 署名作者: Bonnans, J. Frederic; Lavigne, Pierre; Pfeiffer, Laurent
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01934-8
• 发表日期: 2023
• 页码: 241-278
• 关键词: density constraints

摘要

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows hard constraints on the distribution of the agents. We analyze the connection between the MFG problem and two optimal control problems in duality. We present two families of numerical methods and detail their implementation: (i) primal-dual proximal methods (and their extension with nonlinear proximity operators), (ii) the alternating direction method of multipliers (ADMM) and a variant called ADM-G. We give some convergence results. Numerical results are provided for two examples with hard constraints.