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Monotone Solutions of the Master Equation for Mean Field Games with Idiosyncratic Noise

Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2022), Monotone Solutions of the Master Equation for Mean Field Games with Idiosyncratic Noise, SIAM Journal on Mathematical Analysis, 54, 4, p. 4198-4237. 10.1137/21M1450008

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
SIAM Journal on Mathematical Analysis
Volume
54
Number
4
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
4198-4237
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Souganidis, Panagiotis E.
Department of Mathematics [Chicago]
Abstract (EN)
We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work in a monotone setting and rely on Lions' Hilbert space approach. For the first-order master equation without idiosyncratic noise, we also give an equivalent definition in the space of measures and establish the well-posedness.
Subjects / Keywords
mean field games; master equation; weak solutions