Splitting methods and short time existence for the master equations in mean field games

Understand

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player.

• Both problems are infinite dimensional equations stated in the space of probability measures.
• Our new approach simplifies, shortens and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.