  This paper studies singular mean field control problems and singular mean
field stochastic differential games. Both sufficient and necessary conditions
for the optimal controls and for the Nash equilibrium are obtained. Under some
assumptions the optimality conditions for singular mean-field control are
reduced to a reflected Skorohod problem, whose solution is proved to exist
uniquely. Applications are given to optimal harvesting of stochastic mean-field
systems, optimal irreversible investments under uncertainty and to mean-field
singular investment games. In particular, a simple singular mean-field
investment game is studied where the Nash equilibrium exists but is not unique.
