Comptes Rendus
no. 11-12
Partial Differential Equations
On the planning problem for a class of Mean Field Games
[Sur le problème de planification pour une classe de jeux à champ moyen]

Présenté par : Pierre-Louis Lions

Alessio Porretta1
1 Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 457-462.

Nous donnons un résultat dʼexistence et dʼunicité des solutions faibles du problème de planification pour une classe de jeux à champ moyen. Il sʼagit dʼun problème de transport optimal qui consiste en la contrôlabilité exacte au temps T de lʼéquation de Fokker–Planck en utilisant des champs obtenus comme loi feedback optimale dʼune équation de Hamilton–Jacobi–Bellman couplée.

We give a result of existence and uniqueness of weak solutions to the planning problem for a class of Mean Field Games. This is a kind of optimal transportation problem consisting in the exact controllability at time T of Fokker–Planck equations obtained using drifts arising as the optimal feedbacks from a coupled backward Hamilton–Jacobi–Bellman equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.004
Alessio Porretta 1

1 Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy 
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Alessio Porretta. On the planning problem for a class of Mean Field Games. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 457-462. doi : 10.1016/j.crma.2013.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.004/

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[10] A. Porretta, Weak solutions to Fokker–Planck equations and Mean Field Games, in preparation.

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