TL;DR
This paper introduces a quantum version of the Matching Pennies game using an EPR-Bohm setting, revealing new Nash equilibria when quantum probabilities violate Bell's inequality.
Contribution
It constructs a quantum Matching Pennies game without state vectors, embedding the classical game and analyzing quantum correlations' impact on equilibria.
Findings
New Nash equilibria emerge with maximal Bell inequality violation.
Quantum probabilities alter classical game outcomes.
Classical game recovered when probabilities are factorizable.
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 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.
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