Weak solutions for first order mean field games with local coupling

Pierre Cardaliaguet (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise $\epsilon-$Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet. Weak solutions for first order mean field games with local coupling. Bettiol, P., Cannarsa, P., Colombo, G., Motta, M., & Rampazzo, F. Analysis and Geometry in Control Theory and its Applications., 11, 2015, Springer INdAM Series. ⟨hal-00827957⟩