Two-player conflicting interest Bayesian games and Bell nonlocality

TL;DR

This paper introduces three new conflicting interest Bayesian games demonstrating quantum mechanics' advantages, each linked to different Bell inequalities, expanding understanding of nonlocality in quantum game theory.

Contribution

It presents three novel conflicting interest Bayesian games connected to various Bell inequalities, highlighting quantum advantages beyond common interest scenarios.

Findings

Quantum mechanics provides advantages in the new Bayesian games.

Each game is associated with a specific Bell inequality.

The results extend the understanding of nonlocality in conflicting interest games.

Abstract

Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way. Most of these Bayesian games that have been discussed are common interest games. Recently the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with 3 possible measurement outcomes, and the third game is linked with a generalized Bell inequality with 3 possible measurement settings.