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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
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Markus Fischer: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University

No 661, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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 probabiltiy and sub-probability measures.

Keywords: Mean field games; submodularity; complete lattice of measures; Tarki's fixed point theorem; Markov chain; singular stochastic control; refelcted diffusion; optimal stopping. (search for similar items in EconPapers)
Pages: 37
Date: 2022-01-26
New Economics Papers: this item is included in nep-gth and nep-ore
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https://pub.uni-bielefeld.de/download/2960759/2960760 First Version, 2022 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:661

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