  We create a new two-player game on the Sperner Triangle based on Sperner's
lemma. Our game has simple rules and several desirable properties. First, the
game is always certain to have a winner. Second, like many other interesting
games such as Hex and Geography, we prove that deciding whether one can win our
game is a PSPACE-complete problem. Third, there is an elegant balance in the
game such that neither the first nor the second player always has a decisive
advantage. We provide a web-based version of the game, playable at:
http://cs-people.bu.edu/paithan/spernerGame/ . In addition we propose other
games, also based on fixed-point theorems.
