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arXiv:1507.07341 · Physics Letters A

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

Azhar Iqbal, James M. Chappell, Derek Abbott

Published Aug 14, 2018• 8 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2018.08.011

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A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria. A refinement on the set of Pareto optimal outcomes is known as social optimality in which the sum of players' payoffs are maximized. This paper analyzes social optimality in a Bayesian game that uses the setting of generalized Einstein-Podolsky-Rosen experiments for its physical implementation. We show that for the quantum Bayesian game a direct connection appears between the violation of Bell's inequality and the social optimal outcome of the game and that it attains a superior socially optimal outcome.