MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY

By Wilfrid Gangbo; Alpár R. Mészáros; Chenchen Mou; Jianfeng Zhang

doi:10.1214/22-AOP1580

MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY

By Wilfrid Gangbo, Alpár R. Mészáros, Chenchen Mou, Jianfeng Zhang

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.

Original language	English (US)
Pages (from-to)	2178-2217
Number of pages	40
Journal	Annals of Probability
Volume	50
Issue number	6
DOIs	https://doi.org/10.1214/22-AOP1580
State	Published - Nov 1 2022
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-12-07
Acknowledged KAUST grant number(s): ORA-2021-CRG10-4674.2
Acknowledgements: The research of WG was supported by NSF Grant DMS-1700202 and Air Force Grant FA9550-18-1-0502. ARM was partially supported 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 and Hong Kong RGC Grant ECS 9048215. The research of JZ was supported in part by NSF Grant DMS-1908665
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY",

abstract = "In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.",

author = "Gangbo, {By Wilfrid} and M{\'e}sz{\'a}ros, {Alp{\'a}r R.} and Chenchen Mou and Jianfeng Zhang",

note = "KAUST Repository Item: Exported on 2022-12-07 Acknowledged KAUST grant number(s): ORA-2021-CRG10-4674.2 Acknowledgements: The research of WG was supported by NSF Grant DMS-1700202 and Air Force Grant FA9550-18-1-0502. ARM was partially supported 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 and Hong Kong RGC Grant ECS 9048215. The research of JZ was supported in part by NSF Grant DMS-1908665 This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1214/22-AOP1580",

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AU - Mou, Chenchen

AU - Zhang, Jianfeng

N1 - KAUST Repository Item: Exported on 2022-12-07 Acknowledged KAUST grant number(s): ORA-2021-CRG10-4674.2 Acknowledgements: The research of WG was supported by NSF Grant DMS-1700202 and Air Force Grant FA9550-18-1-0502. ARM was partially supported 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 and Hong Kong RGC Grant ECS 9048215. The research of JZ was supported in part by NSF Grant DMS-1908665 This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.

AB - In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.

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JO - Annals of Probability

JF - Annals of Probability

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MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY

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