  Motivated by Buscemi's semi-quantum nonlocal game [PRL 108, 200401(2012)], We
propose an entanglement witness game, a quantum game based on entanglement
witness. Similar as the semi-quantum nonlocal game, the existence of
entanglement shared by the players is necessary and sufficient for obtaining a
positive average payoff in our entanglement witness game. Two explicit examples
are constructed to demonstrate how to play our entanglement witness game and
its relations with the CHSH nonlocal game.
