Cournot-Nash equilibria and optimal transport

  • Date February 26, 2015
  • Hour 4 pm
  • Room GSSI Main Lecture Hall
  • Speaker Adrien Blanchet (Université Toulouse)
  • Area Maths
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 characterisation of the equilibria. Actually the equilibria condition is equivalent to the Euler-Lagrange of a minimisation 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 characterise the equilibrium and give different ways to simulate them numerically.

This is a joint work with G. Carlier