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We introduce a new mean field kinetic model for systems of rational agentsinteracting in a game theoretical framework. This model is inspired fromnon-cooperative anonymous games with a continuum of players and Mean-FieldGames. The large time behavior of the system is given by a macroscopic closurewith a Nash equilibrium serving as the local thermodynamic equilibrium. Anapplication of the presented theory to a social model (herding behavior) isdiscussed.

A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games