Mean field games theory describes the strategic interactions in a large population of similar agents whereas the strategy of the individuals depend on the distribution law of the state. The equilibria solve a system of partial differential equations where a backward Hamilton-Jacobi-Bellman equation for the value function is coupled with a forward Fokker-Planck equation for the mass distribution. If the cost criteria depend on the density of the distribution law, a theory of weak solutions is needed to handle mean field games systems, including new results concerning the Fokker-Planck equation with L-2 drift. Here we prove existence and uniqueness of weak solutions when the dynamics takes place in the whole space RN. We extend previous results obtained so far only for compact state space.
Porretta, A. (2017). On the weak theory for mean field games systems. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 10(3), 411-439 [10.1007/s40574-016-0105-x].
On the weak theory for mean field games systems
Porretta A.
2017-01-01
Abstract
Mean field games theory describes the strategic interactions in a large population of similar agents whereas the strategy of the individuals depend on the distribution law of the state. The equilibria solve a system of partial differential equations where a backward Hamilton-Jacobi-Bellman equation for the value function is coupled with a forward Fokker-Planck equation for the mass distribution. If the cost criteria depend on the density of the distribution law, a theory of weak solutions is needed to handle mean field games systems, including new results concerning the Fokker-Planck equation with L-2 drift. Here we prove existence and uniqueness of weak solutions when the dynamics takes place in the whole space RN. We extend previous results obtained so far only for compact state space.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
