A reference case for mean field games models

Olivier Guéant (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this article, we present a reference case of mean field games. This case can be seen as a reference for two main reasons. First, the case is simple enough to allow for explicit resolution: Bellman functions are quadratic, stationary measures are normal and stability can be dealt with explicitly using Hermite polynomials. Second, in spite of its simplicity, the case is rich enough in terms of mathematics to be generalized and to inspire the study of more complex models that may not be as tractable as this one.

Mots clés: Partial differential equations; Mean field games; Control theory; Numerical methods

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Guéant. A reference case for mean field games models. Journal de Mathématiques Pures et Appliquées, 2009, 92 (3), pp. 276-294. ⟨10.1016/j.matpur.2009.04.008⟩. ⟨hal-01393099⟩