Seminari del Dipartimento di Matematica

Seminario del 2024

Coarse correlated equilibria in mean field games

nell'ambito della serie: STOCHASTICS AND APPLICATIONS - 2024

probabilità

In the context of finite horizon mean field games with continuous time dynamics driven by additive Wiener noise, we introduce a notion of coarse correlated equilibrium in open-loop strategies. For non-cooperative many-player games, a coarse correlated equilibrium can be seen as a lottery on strategy profiles run according to a publicly known mechanism by a moderator who uses the (non-public) lottery outcomes to tell players in private which strategy to play. Players have to decide in advance whether to pre-commit to the mediator's recommendations or to play without seeing them. We justify our definition by showing that any coarse correlated solution of the mean field game induces approximate coarse correlated equilibria for the underlying N-player games. An existence result for coarse correlated mean field game solutions, not relying on the existence of classical solutions, will be given; an explicitly solvable example will be discussed as well. Joint work with Luciano Campi and Federico Cannerozzi (University of Milan "La Statale").