From Mean Field Games To Navier-Stokes Equations

TL;DR

This paper demonstrates the equivalence between certain Mean Field Game models and PDE systems related to compressible Navier-Stokes equations, providing conditions for solvability via Nash Equilibrium existence.

Contribution

It establishes a novel theoretical link between Mean Field Games and Navier-Stokes equations, including solvability conditions.

Findings

Equivalence between Mean Field Games and Navier-Stokes related PDEs

Conditions for PDE solvability via Nash Equilibrium

Theoretical framework connecting game theory and fluid dynamics

Abstract

This work establishes the equivalence between Mean Field Game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash Equilibrium of the Mean Field Game is provided under a set of conditions.