A Unifying Framework for Submodular Mean Field Games

• 成果类型: Article
• 署名作者: Dianetti, Jodi; Ferrari, Giorgio; Fischer, Markus; Nendel, Max
• 署名单位: University of Bielefeld; University of Padua
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1316
• 发表日期: 2023
• 页码: 1679-1710
• 关键词: dynamic-games; approximation; CONVERGENCE; equilibria; EXISTENCE; selection; systems

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.