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
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Mathematical Analysis
MetadataShow full item record
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 / Keywordsmean field games; master equation; weak solutions
Showing items related by title and author.