Abstract:
We consider a non-atomic anonymous game with a continuum of players, or
mean-field game. The agents are heterogeneous and have a pay-off which
depends on congestion and interaction effects. We prove that a
Cournot-Nash equilibrium is the limit when the number of agents goes to
infinity of a Nash equilibrium. We also give some properties of
existence, uniqueness of the equilibria in the potential game case using
optimal transport techniques. We characterise the equilibrium and give
different numerical methods to numerically compute them in the potential
and non-potential case. These results are obtained in collaboration with
P. Mossay, F. Santambrogio and G. Carlier. |