GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS

Mohit Bansil; Alpár R. Mészáros; Chenchen Mou

doi:10.1137/23M1627651

GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS

Mohit Bansil, Alpár R. Mészáros^*, Chenchen Mou

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

In this paper we construct global in time classical solutions to mean field game 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 nonseparable 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 and Mészáros [Comm. Pure Appl. Math., 75 (2022), pp. 2685-2801] and Gangbo et al. [Ann. Probab., 50 (2022), pp. 2178-2217]. © 2025 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	993-1021
Journal	SIAM Journal on Control and Optimization
Volume	63
Issue number	2
Online published	31 Mar 2025
DOIs	https://doi.org/10.1137/23M1627651
Publication status	Published - Apr 2025

Funding

The first author's work was supported by the National Science Foundation Graduate Research Fellowship under grant DGE-1650604. The first and second authors 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.\"\" The second author's work was also partially supported by the EPSRC New Investigator Award ``Mean Field Games and Master Equations\"\" under award EP/X020320/1 and by the King Abdullah University of Science and Technology Research Funding (KRF) under award ORA-2021-CRG10-4674.2. The third author gratefully acknowledges the support by CityU start-up grant 7200684 and by Hong Kong RGC grants ECS 21302521, GRF 11311422, and GRF 11303223.

Research Keywords

absence of idiosyncratic noise
common noise
displacement monotonicity
MFG master equations
nonseparable Hamiltonian

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RGC-funded

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10.1137/23M1627651

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title = "GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS",

abstract = "In this paper we construct global in time classical solutions to mean field game 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 nonseparable 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 and M{\'e}sz{\'a}ros [Comm. Pure Appl. Math., 75 (2022), pp. 2685-2801] and Gangbo et al. [Ann. Probab., 50 (2022), pp. 2178-2217]. {\textcopyright} 2025 Society for Industrial and Applied Mathematics.",

keywords = "absence of idiosyncratic noise, common noise, displacement monotonicity, MFG master equations, nonseparable Hamiltonian",

author = "Mohit Bansil and M{\'e}sz{\'a}ros, {Alp{\'a}r R.} and Chenchen Mou",

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T1 - GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS

AU - Bansil, Mohit

AU - Mészáros, Alpár R.

AU - Mou, Chenchen

PY - 2025/4

Y1 - 2025/4

N2 - In this paper we construct global in time classical solutions to mean field game 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 nonseparable 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 and Mészáros [Comm. Pure Appl. Math., 75 (2022), pp. 2685-2801] and Gangbo et al. [Ann. Probab., 50 (2022), pp. 2178-2217]. © 2025 Society for Industrial and Applied Mathematics.

AB - In this paper we construct global in time classical solutions to mean field game 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 nonseparable 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 and Mészáros [Comm. Pure Appl. Math., 75 (2022), pp. 2685-2801] and Gangbo et al. [Ann. Probab., 50 (2022), pp. 2178-2217]. © 2025 Society for Industrial and Applied Mathematics.

KW - absence of idiosyncratic noise

KW - common noise

KW - displacement monotonicity

KW - MFG master equations

KW - nonseparable Hamiltonian

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GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS

Abstract

Funding

Research Keywords

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GRF: On Some Generalized Mean Field Games

GRF: Mean Field Games with Monotonicity and Anti-monotonicity Conditions

ECS: On Mean Field Game Theory with Non-separable Hamiltonians

Cite this

GLOBAL WELL-POSEDNESS OF DISPLACEMENT MONOTONE DEGENERATE MEAN FIELD GAMES MASTER EQUATIONS

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: On Some Generalized Mean Field Games

GRF: Mean Field Games with Monotonicity and Anti-monotonicity Conditions

ECS: On Mean Field Game Theory with Non-separable Hamiltonians

Cite this