Mild and weak solutions of Mean Field Games problem for linear control systems
Cannarsa, Piermarco; Mendico, Cristian (2020), Mild and weak solutions of Mean Field Games problem for linear control systems, Minimax Theory and its Applications, 5, 2, p. 221-250
TypeArticle accepté pour publication ou publié
Journal nameMinimax Theory and its Applications
MetadataShow full item record
Dipartimento di Matematica [Roma II] [DIPMAT]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Gran Sasso Science Institute [GSSI]
Abstract (EN)The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on Rd. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability measures on the space of admissible trajectories, and mild solutions as solutions associated with such equilibria. Moreover, we prove the existence and uniqueness of mild solutions and we study their regularity: we prove Hölder regularity of Mean Field Games equilibria and fractional semiconcavity for the value function of the underlying optimal control problem. Finally, we address the PDEs system associated with the Mean Field Games problem and we prove that the class of mild solutions coincides with a suitable class of weak solutions.
Subjects / KeywordsMean field games; mean field games equilibrium; semiconcave estimates; control systems
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Cannarsa, Piermarco; Capuani, Rossana; Cardaliaguet, Pierre (2021) Article accepté pour publication ou publié