Italo Capuzzo Dolcetta
(Roma, Italy)

A numerical approach to mean field games

Mean fields games models introduced by Lasry-Lions describe through new systems of pde’s the asymptotic behavior of differential games in which the number of players tends to +∞. In the talk we discuss some recent work in collaboration with Y. Achdou and F. Camilli about numerical methods for the approximation of stationary and nonstationary versions of such models. Particular attention will be given to the optimal planning problem, in which the positions of a very large number of identical rational agents, with common value function, evolve from an initial given spatial density to a desired target density at the final horizon time.