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.
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.
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Alessio Porretta 1
@article{CRMATH_2013__351_11-12_457_0, author = {Alessio Porretta}, title = {On the planning problem for a class of {Mean} {Field} {Games}}, journal = {Comptes Rendus. Math\'ematique}, pages = {457--462}, publisher = {Elsevier}, volume = {351}, number = {11-12}, year = {2013}, doi = {10.1016/j.crma.2013.07.004}, language = {en}, }
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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