Mean Field Games with a Quadratic Hamiltonian: A Constructive Scheme

Olivier Guéant (1)

1 LJLL - Laboratoire Jacques-Louis Lions

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to infinity, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in the case of a quadratic Hamiltonian. This system is then used to exhibit a monotonic scheme to build solutions of the MFG equations. Effective numerical methods based on this constructive scheme are presented and numerical experiments are carried out.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Guéant. Mean Field Games with a Quadratic Hamiltonian: A Constructive Scheme. Annals of the International Society of Dynamic Games, 12, Springer, pp. 229-241, 2013, Advances in Dynamic Games. ⟨hal-01393106⟩