Markus Fischer: Correlated equilibria and mean field games

Abstract

Mean field games are limit models for symmetric N-player games, as N tends to infinity, where the prelimit models are solved in terms of Nash equilibria. A generalization of the notion of Nash equilibrium, due to Robert Aumann (1974, 1987), is that of correlated equilibrium. In a simple discrete, non-static setting, we will discuss mean field games based on correlated equilibria. We give a definition of correlated mean field game solution, prove that it arises as limit of symmetric N-player correlated equilibria in restricted Markov open-loop strategies, and construct approximate N-player equilibria starting from a correlated mean field game solution. We also compare our definition to the one by D. Lacker of weak solutions for mean field games without common noise, and give an example of correlated mean field game solutions with non-deterministic flow of measures.

This is joint work with Luciano Campi, University of Milan "La Statale".

Zoom notes: This meeting ID – 621 4469 8204 – will be the recurring meeting for the Statistics and Probability Seminar.