Mean Field Games with Singular Controls

Abstract

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 càdlàg functions.

33 pages

References in corpus (3)

• Mean field games via controlled martingale problems: Existence of Markovian equilibria
• Singular mean-field control games with applications to optimal harvesting and investment problems
• Approximation of Mean Field Games to N-Player Stochastic Games, with Singular Controls