In this paper we establish a new connection between a class of 2-player nonzerosum

games of optimal stopping and certain 2-player nonzero-sum games of singular control. We

show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at

two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of

singular control. Moreover a differential link between the players' value functions holds across

the two games.