Large-scale dynamics of Mean-Field Games driven by local Nash equilibria (previously : A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games)

Pierre Degond (1) , Jian-Guo Liu (2) , Christian Ringhofer (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Department of Physics and Department of Mathematics
3 Department of Mathematics

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.

Domaines: Physique mathématique [math-ph]

Pierre Degond, Jian-Guo Liu, Christian Ringhofer. Large-scale dynamics of Mean-Field Games driven by local Nash equilibria (previously : A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games). Journal of Nonlinear Science, 2014, 24 (1), pp.93-115. ⟨10.1007/s00332-013-9185-2⟩. ⟨hal-00768824⟩