A Unifying Framework for Submodular Mean Field Games

被引:9
作者
Dianetti, Jodi [1 ]
Ferrari, Giorgio [1 ]
Fischer, Markus [2 ]
Nendel, Max [1 ]
机构
[1] Bielefeld Univ, Ctr Math Econ, D-33613 Bielefeld, Germany
[2] Univ Padua, Dept Math Tullio Levi Civita, I-35121 Padua, Italy
关键词
mean field games; submodularity; complete lattice of measures; Tarski's fixed point theorem; Markov chain; singular stochastic control; reflected diffusion; optimal stopping; DYNAMIC-GAMES; APPROXIMATION; CONVERGENCE; EQUILIBRIA; EXISTENCE; SELECTION; SYSTEMS;
D O I
10.1287/moor.2022.1316
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
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.
引用
收藏
页码:1679 / 1710
页数:32
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