A Unifying Framework for Submodular Mean Field Games

Jodi Dianetti (), Giorgio Ferrari (), Markus Fischer () and Max Nendel ()
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Jodi Dianetti: Center for Mathematical Economics, Bielefeld University, D-33615 Bielefeld, Germany
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University, D-33615 Bielefeld, Germany
Markus Fischer: Department of Mathematics “Tullio Levi-Civita,” University of Padua, 35121 Padova, Italy
Max Nendel: Center for Mathematical Economics, Bielefeld University, D-33615 Bielefeld, Germany

Mathematics of Operations Research, 2023, vol. 48, issue 3, 1679-1710

Abstract: 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.

Keywords: Primary: 49N80; 91A16; secondary: 93E20; 06B23; mean field games; submodularity; complete lattice of measures; Tarski’s fixed point theorem; Markov chain; singular stochastic control; reflected diffusion; optimal stopping (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:3:p:1679-1710

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