Multistage games and Bell scenarios with communication

TL;DR

This paper extends the connection between Bell nonlocality and Bayesian games to multistage games with communication, analyzing how quantum correlations influence equilibria in complex strategic scenarios.

Contribution

It generalizes the link between Bell scenarios and Bayesian games to multistage settings with communication, providing a new framework for analyzing quantum advantages.

Findings

Quantum nonlocal correlations can alter equilibrium outcomes in multistage games.

The framework applies to specific cases demonstrating quantum advantage.

Communication of measurement outcomes influences strategic equilibria.

Abstract

Bell nonlocality is a cornerstone of quantum theory with applications in information processing ranging from cryptography to distributed computing and game theory. Indeed, it is known that Bell's theorem can be formally linked to Bayesian games, allowing the use of nonlocal correlations to advise players and thereby achieve new points of equilibrium that are unavailable classically. Here we generalize this link, proving the connection between multistage games of incomplete information with Bell scenarios involving the communication of measurement outcomes between the parties. We apply the general framework for a few cases of interest and analyze the equilibrium reached by quantum nonlocal correlations.