Finite Horizon Mean Field Games on Networks - Institut de Recherche Mathématiques de Rennes Accéder directement au contenu
Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2020

Finite Horizon Mean Field Games on Networks

Manh-Khang Dao
  • Fonction : Auteur
  • PersonId : 1011025
Olivier Ley

Résumé

We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The value function u is continuous and satisfies general Kirchhoff conditions at the vertices. The density m of the distribution of states satisfies dual transmission conditions: in particular, m is generally discontinuous across the vertices, and the values of m on each side of the vertices satisfy special compatibility conditions. The stress is put on the case when the Hamiltonian is Lipschitz continuous. Existence and uniqueness are proven.
Fichier principal
Vignette du fichier
MFG-nonstat-hal.pdf (471.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02058824 , version 1 (06-03-2019)

Identifiants

Citer

Yves Achdou, Manh-Khang Dao, Olivier Ley, Nicoletta Tchou. Finite Horizon Mean Field Games on Networks. Calculus of Variations and Partial Differential Equations, 2020, 59 (5), pp.article n°157. ⟨10.1007/s00526-020-01816-3⟩. ⟨hal-02058824⟩
304 Consultations
167 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More