Social optimality in quantum Bayesian games

TL;DR

This paper explores social optimality in quantum Bayesian games, demonstrating a link between Bell's inequality violation and improved social outcomes using quantum strategies.

Contribution

It introduces a quantum Bayesian game framework based on EPR experiments and connects Bell inequality violations to social optimality.

Findings

Bell inequality violation correlates with better social outcomes

Quantum strategies can achieve superior social optimality

The framework links quantum physics with game-theoretic solution concepts

Abstract

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.