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Main Authors: Ferreira, Rita, Gomes, Diogo, Tada, Teruo
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2502.20091
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author Ferreira, Rita
Gomes, Diogo
Tada, Teruo
author_facet Ferreira, Rita
Gomes, Diogo
Tada, Teruo
contents This chapter examines monotonicity techniques in the theory of mean-field games(MFGs). Originally, monotonicity ideas were used to establish the uniqueness of solutions for MFGs. Later, monotonicity methods and monotone operators were further exploited to build numerical methods and to construct weak solutions under mild assumptions. Here, after a brief discussion on the mean-field game formulation, we introduce the Minty method and regularization strategies for PDEs. These are then used to address typical stationary and time-dependent monotone MFGs and to establish the existence of weak solutions for such MFGs.
format Preprint
id arxiv_https___arxiv_org_abs_2502_20091
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An introduction to monotonicity methods in mean-field games
Ferreira, Rita
Gomes, Diogo
Tada, Teruo
Analysis of PDEs
This chapter examines monotonicity techniques in the theory of mean-field games(MFGs). Originally, monotonicity ideas were used to establish the uniqueness of solutions for MFGs. Later, monotonicity methods and monotone operators were further exploited to build numerical methods and to construct weak solutions under mild assumptions. Here, after a brief discussion on the mean-field game formulation, we introduce the Minty method and regularization strategies for PDEs. These are then used to address typical stationary and time-dependent monotone MFGs and to establish the existence of weak solutions for such MFGs.
title An introduction to monotonicity methods in mean-field games
topic Analysis of PDEs
url https://arxiv.org/abs/2502.20091