## Correlated equilibria in mean-field games

#### Luciano CampiLondon School of Economics and Political Science

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 non-static 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 compare our definition to the one by Lacker (2018) of weak solutions for mean field games without a common noise. This talk is based on a joint work with Markus Fischer (Padova University).

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