A unifying framework for submodular mean field games

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 661

Classification and Topics

• Classification: Wirtschaft
• Subject: Mean field games ; submodularity ; complete lattice of measures ; Tarski's fixedpoint theorem ; Markov chain ; singular stochastic control ; reflected diffusion ; optimal stopping

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Dianetti, Jodi ; Ferrari, Giorgio ; Fischer, Markus ; Nendel, Max
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2022

Further information

• Handle: http://hdl.handle.net/10419/249884
• URN: urn:nbn:de:0070-pub-29607594
• Last update: 10.03.2025, 11:44 AM CET