A Unifying Framework for Submodular Mean Field Games
提出了子模平均场博弈的抽象框架，给出了可验证的充分条件，证明在数据可能不连续且允许共同噪声的模型中强平均场均衡的存在性和近似性，适用于离散时间有限空间马尔可夫链、奇异控制和反射扩散等问题。
We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow us to prove the existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is allowed. The setting is general enough to encompass qualitatively different problems, such as mean field games for discrete time finite space Markov chains, singularly controlled and reflected diffusions, and mean field games of optimal timing. Our analysis hinges on Tarski’s fixed point theorem, along with technical results on lattices of flows of probability and subprobability measures. Funding: Financial support by the German Research Foundation [Collaborative Research Centre Grant 1283/2 2021–317210226] is acknowledged.