  A quantum version of the Matching Pennies (MP) game is proposed that is
played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct
the quantum game without using the state vectors, while considering only the
quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We
embed the classical game within the quantum game such that the classical MP
game results when the quantum mechanical joint probabilities become
factorizable. We report new Nash equilibria in the quantum MP game that emerge
when the quantum mechanical joint probabilities maximally violate the
Clauser-Horne-Shimony-Holt form of Bell's inequality.
