Cournot--Nash Equilibrium and Optimal Transport in a Dynamic Setting

We consider a large population dynamic game in discrete time. The peculiarity of the is that players are characterized by time-evolving types, and so reasonably their actions should not anticipate future values types. When interactions between mean field kind, we relate Nash equilibria for such games to an asymptotic notion Cournot--Nash equilibria. Inspired works Blanchet Carlier static situation, interpret light causal optimal transport theory. Further specializing potential type, establish existence, uniqueness, characterization Moreover develop, first time, numerical scheme transport, which then leveraged order compute This illustrated detailed case study congestion game.