  We study a class of zero-sum games between a singular-controller and a
stopper over finite-time horizon. The underlying process is a multi-dimensional
(locally non-degenerate) controlled stochastic differential equation (SDE)
evolving in an unbounded domain. We prove that such games admit a value and
provide an optimal strategy for the stopper. The value of the game is shown to
be the maximal solution, in a suitable Sobolev class, of a variational
inequality of `min-max' type with obstacle constraint and gradient constraint.
Although the variational inequality and the game are solved on an unbounded
domain we do not require boundedness of either the coefficients of the
controlled SDE or of the cost functions in the game.
