Mean Field Games with Singular Controls

Guanxing Fu, Ulrich Horst

Published 2016-12-16Version 1

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. As a by-product, we obtain an existence of relaxed solutions results for McKean- Vlasov stochastic singular control problems. Finally, we prove that the solutions to a particular class of MFGs with singular controls can be approximated by the solutions to MFGs with purely regular control. Our existence and approximation results strongly hinge on the use of the Skorokhod $M1$ topology on the space of c\`adl\`ag functions.