Correlated Equilibria for Mean Field Games with Progressive Strategies

In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.Funding: O. Bonesini acknowledges financial support from Engineering and Physical Sciences Research Council [Grant EP/T032146/1]. M. Fischer acknowledges partial support through the University of Padua [Research Project BIRD229791 “Stochastic mean field control and the Schrödinger problem”].