  We analyze the computational complexity of two 2-player games involving
packing objects into a box. In the first game, players alternate drawing
polycubes from a shared pile and placing them into an initially empty box in
any available location; the first player who can't place another piece loses.
In the second game, there is a fixed sequence of polycubes, and on a player's
turn they drop the next piece in through the top of the box, after which it
falls until it hits a previously placed piece (as in Tetris); the first player
who can't place the next piece loses. We prove that in both games, deciding the
outcome under perfect play is PSPACE-complete.
