Mean Field Games on Networks

Claudio Marchi (Padova, Italy)

We consider stationary Mean Field Games (briefly, MFG) defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal  control interpretation of the problem.

First, we prove separately the well-posedness of each of the two equations  composing the MFG system. After we prove existence and uniqueness of the  solution to the MFG system.

Finally, we propose some numerical methods, proving the well-posedness and  the converging of the scheme.

These are joint works with F. Camilli and S. Cacace.

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