Advances in Mathematical Finance and Optimal Transport

# Correlated equilibria and mean field games

speaker: Luciano Campi (Università degli Studi di Milano)

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 (1973, 1987), is that of a correlated equilibrium. Here, we discuss, in a simple discrete time setting, the mean field game limit for correlated equilibria. We give a definition of correlated mean field game solution, prove that it arises as limit of N-player correlated equilibria in restricted (”open-loop”) Markov feedback strategies, and show how to construct approximate N-player equilibria starting from a correlated mean field game solution. We also show how to adapt the definition of correlated solution to the case where the players in the pre-limit game are allowed to deviate following semi-Markov strategies, i.e. depending on the other players’ states via the empirical measure. This talk is based on joint works with Ofelia Bonesini and Markus Fischer (Padova University).

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