A Unifying Framework for Submodular Mean Field Games

DOI10.1287/MOOR.2022.1316arXiv2201.07850MaRDI QIDQ6121643

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Publication date: 27 February 2024

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Abstract: We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove 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 sub-probability measures.

Full work available at URL: https://arxiv.org/abs/2201.07850

zbMATH Keywords

optimal stoppingsubmodularityMarkov chainTarski's fixed point theoremsingular stochastic controlmean field gamesreflected diffusioncomplete lattice of measures

Mathematics Subject Classification ID

Optimal stochastic control (93E20) Complete lattices, completions (06B23) Mean field games and control (49N80) Mean field games (aspects of game theory) (91A16)

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