Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations

Type
Preprint

Authors
Bansil, Mohit
Mészáros, Alpár R.
Mou, Chenchen

KAUST Grant Number
ORA-2021-CRG10-4674.2

Date
2023-08-30

Abstract
In this manuscript we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include both deterministic models and dynamics driven solely by a Brownian common noise. We consider a general class of non-separable Hamiltonians and final data functions that are supposed to be displacement monotone. Our main results unify and generalize in particular some of the well-posedness results on displacement monotone master equations obtained recently by Gangbo--M'esz'aros and Gangbo--M'esz'aros--Mou--Zhang.

Acknowledgements
MB’s work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650604. MB and ARM acknowledge the support of the Heilbronn Institute for Mathematical Research and the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences through the focused research grant “The master equation in Mean Field Games”. ARM has also been partially supported by the EPSRC New Investigator Award “Mean Field Games and Master equations” under award no. EP/X020320/1 and by the King Abdullah University of Science and Technology Research Funding (KRF) under award no. ORA-2021-CRG10-4674.2. CM gratefully acknowledges the support by CityU Start-up Grant 7200684, Hong Kong RGC Grant ECS 21302521, Hong Kong RGC Grant GRF 11311422 and Hong Kong RGC Grant GRF 11303223.

Publisher
arXiv

arXiv
2308.16167

Additional Links
https://arxiv.org/pdf/2308.16167.pdf

Permanent link to this record