Coarse correlated equilibria for mean field games in open loop strategies

Campi Luciano, University of Milan
Cannerozzi Federico, University of Milan
Fischer Markus, Università degli Studi di Padova

Despite their popularity, Nash equilibria (NE) are not the only notion of equilibria for N-player games. A good alternative is given by coarse correlated equilibria (CCE), as they may lead to higher payoffs than NE and they arise more naturally as the outcomes of learning algorithms. CCEs feature a moderator who randomly selects a strategy profile for the N-players, correlating their strategies without requiring them to cooperate. In the context of continuous time mean field games (MFGs) in stochastic open loop strategies, we introduce the notion of coarse correlated solution, which can be seen as the mean field counterpart of CCEs in the N-player game. We justify our definition by showing that any coarse correlated solution of the MFG induces approximate CCEs with vanishing error for the underlying N-player games. An existence result for coarse correlated solutions of the MFG will be given, by means of a minimax theorem. Finally, an explicitly solvable example will be discussed as well. This talk is based on the joint work with Luciano Campi(University of Milan) and Markus Fischer (University of Padua).

Area: CS2 - Mean Field Games and Mean Field Control I (Jodi Dianetti & Mattia Martini)

Keywords: Mean field games

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