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

TL;DR

This paper develops a macroscopic closure model for kinetic systems of rational agents in mean-field game settings, linking microscopic interactions to Nash equilibria and demonstrating its application to social herding behavior.

Contribution

It introduces a novel kinetic model with a Nash equilibrium-based macroscopic closure for systems of agents in mean-field games, bridging microscopic and macroscopic descriptions.

Findings

Large time behavior characterized by Nash equilibrium

Application to social herding behavior modeled successfully

Provides a new framework for kinetic mean-field game analysis

Abstract

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.