  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.
