Mean field games equations with quadratic Hamiltonian: a specific approach

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.

Mots clés: Mean field games; constructive scheme; numerical methods

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Olivier Guéant. Mean field games equations with quadratic Hamiltonian: a specific approach. Mathematical Models and Methods in Applied Sciences, 2012, 22 (9), ⟨10.1142/S0218202512500224⟩. ⟨hal-01393107⟩