Splitting methods and short time existence for the master equations in mean field games
Cardaliaguet, Pierre; Cirant, Marco; Porretta, Alessio (2020), Splitting methods and short time existence for the master equations in mean field games. https://basepub.dauphine.fr/handle/123456789/20667
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02454135
Cahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / Keywordsmean field games theory
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