Social optimality in quantum Bayesian games

• Study game-theoretic solution concept of social optimality in a quantum Bayesian game.
• Our quantum Bayesian game uses the setting of generalized EPR experiments.
• A new stronger socially optimal outcome emerges in the quantum Bayesian game.

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 is 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.