Constructing quantum games from a system of Bell's inequalities

TL;DR

This paper presents a method to construct quantum games directly from Bell's inequalities, linking quantum correlations with game theory and addressing previous criticisms of quantum game formulations.

Contribution

It introduces a novel approach using Bell's inequalities to build quantum games, providing a rigorous foundation and practical examples like Prisoners' Dilemma.

Findings

Quantum games can be constructed from Bell's inequalities.

This approach addresses criticisms of quantum game models.

Examples demonstrate the method's applicability.

Abstract

We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses some of their well known criticisms.