Translation invariant mean field games with common noise

TL;DR

This paper studies a special class of mean field games with common noise, where convolution structure allows transforming solutions from simpler models without common noise, facilitating analysis and solution construction.

Contribution

It introduces a convolution-based structural condition in mean field games with common noise, enabling solution derivation from models without common noise.

Findings

Transformation links solutions with and without common noise

Convolution structure simplifies mean field game analysis

Provides a tractable method for solving complex mean field games

Abstract

This note highlights a special class of mean field games in which the coefficients satisfy a convolution-type structural condition. A mean field game of this type with common noise is related to a certain mean field game without common noise by a simple transformation, which permits a tractable construction of a solution of the problem with common noise from a solution of the problem without.