The complexity of checkers on an N × N board

We consider the game of Checkers generalized to an N × N board. Although certain properties of positions are efficiently computable (e.g., can Black jump all of White\´s pieces in a single move?), the general question, given a position, of whether a specified player can force a win against best play by his opponent, is shown to be PSPACE-hard. Under certain reasonable assumptions about the "drawing rule" in force, the problem is itself in PSPACE and hence is PSPACE-complete.