Adrian Blanchet: Cournot-Nash equilibria and optimal transport

We are interested in Cournot-Nash equilibria in an anonymous, non-atomic game with a continuum of players. We will prove that these equilibria can be seen as the limit of Nash equilibria in pure or mixed strategies. We will also prove existence and uniqueness results in the separable case using an energy characterization of the equilibria. Actually the equilibria condition is equivalent to the Euler-Lagrange of a minimization problem. In the case of congestion effect, this energy is not convex is the usual sense but is convex in the sense of optimal transport. We will also characterize the equilibrium and give different way to simulate them numerically.

This is joint work with G. Carlier

Full report