Here is a game that can be played on a chessboard using a pawn and a queen. One player places either the pawn or the queen on any square on the board, and the other places the other piece on any square that is at least three squares distant from the first piece. The players then take turns moving the queen according to the usual rules of chess (the queen moves any number of squares horizontally, vertically, or diagonally) except that each move must bring the queen closer to the pawn. The pawn does not move during the game. The player who is able to capture the pawn (by moving the queen onto the square occupied by the pawn) wins.
Is there a winning strategy for either player?