Thumbnail

Splitting methods and short time existence for the master equations in mean field games

Cardaliaguet, Pierre; Cirant, Marco; Porretta, Alessio (2022), Splitting methods and short time existence for the master equations in mean field games, Journal of the European Mathematical Society, p. 70. 10.4171/JEMS/1227

View/Open
Type
Article accepté pour publication ou publié
Date
2022
Journal name
Journal of the European Mathematical Society
Publisher
European Mathematical Society
Published in
Paris
Pages
70
Publication identifier
Metadata
Show full item record
Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Cirant, Marco
Porretta, Alessio
Dipartimento di Matematica [Roma II] [DIPMAT]
Abstract (EN)
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite dimensional equations stated in the space of probability measures. Our new approach simplifies, shortens and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.
Subjects / Keywords
mean field games theory