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Mild and weak solutions of Mean Field Games problem for linear control systems

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1907.02654.pdf (278.1Kb)
Date
2020
Dewey
Analyse
Sujet
Mean field games; mean field games equilibrium; semiconcave estimates; control systems
Journal issue
Minimax Theory and its Applications
Volume
5
Number
2
Publication date
2020
Article pages
221-250
Publisher
Heldermann Verlag
URI
https://basepub.dauphine.fr/handle/123456789/21086
Collections
  • CEREMADE : Publications
Metadata
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Author
Cannarsa, Piermarco
15788 Dipartimento di Matematica [Roma II] [DIPMAT]
Mendico, Cristian
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
262452 Gran Sasso Science Institute [GSSI]
Type
Article accepté pour publication ou publié
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.

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