Type
ArticleKAUST Grant Number
ORA-2021-CRG10-4674.2Date
2023-07-13Permanent link to this record
http://hdl.handle.net/10754/682335
Metadata
Show full item recordAbstract
In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for unconditional uniqueness that is independent of the length of the time horizon, the regularity of the starting distribution of the agents, or the regularization effect of a non-degenerate idiosyncratic noise. Through a rich class of simple examples we show that these new conditions are not only in dichotomy with each other, but also with the two widely studied monotonicity conditions in the literature, the Lasry–Lions monotonicity and displacement monotonicity conditions.Citation
Graber, P. J., & Mészáros, A. R. (2023). On monotonicity conditions for Mean Field Games. Journal of Functional Analysis, 110095. https://doi.org/10.1016/j.jfa.2023.110095Sponsors
PJG acknowledges the support of the National Science Foundation through NSF Grants DMS-2045027 and DMS-1905449. We 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 via the NIA with grant number EP/X020320/1 and by the King Abdullah University of Science and Technology Research Funding (KRF) under Award No. ORA-2021-CRG10-4674.2. Last but not least, we would like to thank the referee for their careful reading of our manuscript and for the important comments they gave.Publisher
Elsevier BVJournal
Journal of Functional AnalysisarXiv
2210.02281Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0022123623002525ae974a485f413a2113503eed53cd6c53
10.1016/j.jfa.2023.110095