Existence of solutions of the master equation in the smooth case

TL;DR

This paper provides an alternative proof for the short time existence of solutions to the master equation, a fundamental result in the theory of mean field games.

Contribution

It offers a new proof approach for the existence theorem of the master equation in the smooth case, enhancing understanding of solution existence.

Findings

Established short time existence of solutions for the master equation.

Provided a different proof method from previous work.

Confirmed the robustness of solution existence in the smooth setting.

Abstract

We give a different proof of a theorem of W. Gangbo and A. Swiech on the short time existence of solutions of the master equation.