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GdT CalVa A. Meszaros
Lundi 14 septembre 2015
Alpár Mészáros (Université Paris-Sud, Orsay)
Mean Field Games with density constraints : pressure equals price
Résumé : Motivated by some question recently raised by F. Santambrogio, in this talk we study Mean Field Game systems (of J.-M. Lasry and P.-L. Lions) under density constraints as optimality conditions of two optimization problems in duality. In particular, these problems recall the so-called Benamou-Brenier dynamical formulation of the Monge-Kantorovich optimal transport problem. A weak solution of the system contains an extra term, an additional price imposed on the saturated zones. We show that this price corresponds to the pressure field from the models of incompressible Euler’s equations à la Brenier. By this observation we manage to obtain a minimal regularity, which allows to write optimality conditions at the level of single agent trajectories and to define a weak notion of Nash equilibrium for our model. The talk is based on a joint work with P. Cardaliaguet and F. Santambrogio.
Mise à jour effectuée par
C.David - 26/10/17