  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.
