  This paper establishes the existence of relaxed solutions to mean field games
(MFGs for short) with singular controls. We also prove approximations of
solutions results for a particular class of MFGs with singular controls by
solutions, respectively control rules, for MFGs with purely regular controls.
Our existence and approximation results strongly hinge on the use of the
Skorokhod $M_1$ topology on the space of c\`adl\`ag functions.

Optimization and Control