A Nash equilibrium macroscopic closure for kinetic models coupled with   Mean-Field Games
  We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed. 
Pierre Degond (IMT), Jian-Guo Liu, Christian Ringhofer
math-ph math.MP