Bell nonlocality and Bayesian game theory

TL;DR

This paper explores how Bell nonlocality can enhance Bayesian game strategies by enabling players to use quantum or no-signaling correlations as advice, leading to novel equilibria and advantages over classical approaches.

Contribution

It establishes a connection between Bell nonlocality and Bayesian game theory, introducing the concept of nonlocal advice and quantum/no-signaling Nash equilibria.

Findings

Quantum and no-signaling resources provide strategic advantages in Bayesian games.

New equilibrium concepts based on nonlocal correlations are introduced.

The study proposes analyzing nonlocal advantage through multiple Bell expressions.

Abstract

We discuss a connection between Bell nonlocality and Bayesian games. This link offers interesting perspectives for Bayesian games, namely to allow the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signaling boxes. The possibility of having such 'nonlocal advice' will lead to novel joint strategies, impossible to achieve in the classical setting. This implies that quantum resources, or more general no-signaling resources, offer a genuine advantage over classical ones. Moreover, some of these strategies can represent equilibrium points, leading to the notion of quantum/no-signaling Nash equilibrium. Finally we describe new types of question in the study of nonlocality, namely the consideration of non-local advantage when there is a set of Bell expressions.