Closing In

This is a 2-player paper and pencil game played on a grid of 6 squares by 6 squares. The first turn is slightly different from the following turns: on the first turn the first player writes his initial in any square, as does the second player (though this could not be the square initialed by the first player). On the second and subsequent turns each player 1) fills in the square in which he had previously put his initial and 2) initials another square which is a queen's move from the square which he has just filled in (initialed and filled in squares are barriers to this process). A player loses when he is no longer able to play.