A study of common noise in mean field games

TL;DR

This paper investigates mean field games master equations with common noise, examining how the noise interacts with game dynamics and the implications of monotonicity assumptions on the coefficients.

Contribution

It introduces a framework for analyzing master equations with state-dependent common noise and explores the relationships between different monotonicity regimes.

Findings

Established links between common noise and traditional noise models

Analyzed the impact of monotonicity assumptions on solutions

Provided insights into the structure of master equations with common noise

Abstract

This paper is concerned with the study of mean field games master equations involving an additional variable modelling common noise. We address cases in which the dynamics of this variable can depend on the state of the game, which requires in general additional monotonicity assumptions on the coefficients. We explore the link between such a common noise and more traditional ones, as well as the links between different monotone regimes for the master equation.