We consider an anonymous game with a continuum of players which takes into account congestion and interaction effects. This model was first developed by Beckmann (1976) in an urban equilibrium framework. We also consider a generalisation of this model to the case when agents are inhomogeneous and characterised by a given type.
We prove that these games are actually potential games, so that the Nash equilibrium is equal to the minimiser of an hidden potential. This potential is not convex in the usual sense but along generalised geodesics in the context of optimal transport. This allows us to prove the existence and uniqueness of the equilibrium and to characterise the equilibrium by a partial differential equation which can be solved numerically. We also perform a welfare analysis an describe the welfare transfer needed to restore the efficiency of the game.
This talk will be based of a series of work in collaboration with Carlier, Santambrogio, Mossay and Nenna.
References:
http://www.tse-fr.eu/articles/existence-and-uniqueness-equilibrium-spatial-model-social-interactions
http://www.tse-fr.eu/articles/optimal-transport-and-cournot-nash-equilibria