A Unifying Framework for Submodular Mean Field Games

Dianetti J, Ferrari G, Fischer M, Nendel M (2022) Center for Mathematical Economics Working Papers; 661.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.

AMS (2020)subject classification: 49N80, 91A16, 93E20, 06B23.
Stichworte
Mean field games; submodularity; complete lattice of measures; Tarki's fixed point theorem; Markov chain; singular stochastic control; refelcted diffusion; optimal stopping.
Erscheinungsjahr
2022
Serientitel
Center for Mathematical Economics Working Papers
Band
661
Seite(n)
37
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2960759

Zitieren

Dianetti J, Ferrari G, Fischer M, Nendel M. A Unifying Framework for Submodular Mean Field Games. Center for Mathematical Economics Working Papers. Vol 661. Bielefeld: Center for Mathematical Economics; 2022.
Dianetti, J., Ferrari, G., Fischer, M., & Nendel, M. (2022). A Unifying Framework for Submodular Mean Field Games (Center for Mathematical Economics Working Papers, 661). Bielefeld: Center for Mathematical Economics.
Dianetti, J., Ferrari, G., Fischer, M., and Nendel, M. (2022). A Unifying Framework for Submodular Mean Field Games. Center for Mathematical Economics Working Papers, 661, Bielefeld: Center for Mathematical Economics.
Dianetti, J., et al., 2022. A Unifying Framework for Submodular Mean Field Games, Center for Mathematical Economics Working Papers, no.661, Bielefeld: Center for Mathematical Economics.
J. Dianetti, et al., A Unifying Framework for Submodular Mean Field Games, Center for Mathematical Economics Working Papers, vol. 661, Bielefeld: Center for Mathematical Economics, 2022.
Dianetti, J., Ferrari, G., Fischer, M., Nendel, M.: A Unifying Framework for Submodular Mean Field Games. Center for Mathematical Economics Working Papers, 661. Center for Mathematical Economics, Bielefeld (2022).
Dianetti, Jodi, Ferrari, Giorgio, Fischer, Markus, and Nendel, Max. A Unifying Framework for Submodular Mean Field Games. Bielefeld: Center for Mathematical Economics, 2022. Center for Mathematical Economics Working Papers. 661.
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2022-01-26T09:00:49Z
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