Correlated Equilibria and Mean Field Games: A Simple Model

In the context of simple finite-state discrete time systems, we introduce a generalization of a mean field game solution, called a correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of a solution is justified in two ways: we prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying N-player games, and we show how to construct approximate N-player correlated equilibria starting from a correlated solution to the mean field game.