  Since its introduction by P.L. Lions in his lectures and seminars at the
College de France, see [9], and also the very helpful notes of Cardialaguet [4]
on Lions' lectures, the Master Equation has attracted a lot of interest, and
various points of view have been expressed, see for example Carmona-Delarue
[5], Bensoussan-Frehse-Yam [2], Buckdahn-Li-Peng-Rainer [3]. There are several
ways to introduce this type of equation; and in those mentioned works, they
involve an argument which is a probability measure, while P.L. Lions has
recently proposed the idea of working with the Hilbert space of square
integrable random variables. Hence writing the equation is an issue; while
another issue is its origin. In this article, we discuss all these various
aspects, and our modeling argument relies heavily on a seminar at College de
France delivered by P.L. Lions on November 14, 2014.
