Quantum matching pennies game

Abstract

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 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.