New numerical methods for mean field games with quadratic costs

Olivier Guéant (1)

1 LJLL - Laboratoire Jacques-Louis Lions

Mean field games have been introduced by J.-M. Lasry and P.-L. Lions as the limit case of stochastic dierential games when the number of players goes to infinity. In the case of quadratic costs, we present two changes of variables that allow to transform the mean field games (MFG) equations into two simpler systems of equations. The first change of variables, already introduced in a preceding paper, leads to two heat equations with nonlinear source terms. The second change of variables, which is introduced for the first time in this paper, leads to two Hamilton-Jacobi-Bellman equations. Numerical methods based on these equations are presented and numerical experiments are carried out.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Olivier Guéant. New numerical methods for mean field games with quadratic costs. Networks and Heterogenous Media, 2012, 7 (2), pp.315-336. ⟨10.3934/nhm.2012.7.315⟩. ⟨hal-01393108⟩