Section: New Results

Cournot-Nash equilibria

Carlier, Guillaume and Blanchet, Adrien

[24]

The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of N player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. It is therefore natural to investigate the continuous limit as N tends to infinity and to investigate whether it corresponds to the notion of Cournot-Nash equilibria. In [9] , this kind of convergence result is studied in a Wasserstein framework. In [BC1], we go one step further by giving a class of games with a continnum of players for which equilibria may be found as minimizers as a functional on measures which is very similar to the one-step JKO case, uniqueness results are the obtained from displacement convexity arguments. Finally, in [9] some situations which are non variational are considered and existence is obtained by methods combining fixed point arguments and optimal transport.