Constructing multi-player quantum games from non-factorizable joint probabilities

TL;DR

This paper explores how non-factorizable joint probabilities in a three-player EPR setting can alter outcomes of symmetric quantum games, specifically enabling escape from classical dilemmas like Prisoner's Dilemma.

Contribution

It introduces a method to construct multi-player quantum games using non-factorizable probabilities, extending previous two-player results to three-player scenarios.

Findings

Non-factorizable probabilities can change three-player game outcomes.

Players can escape classical Prisoner's Dilemma using quantum correlations.

Contrasts with two-player case where non-factorizability doesn't help escape classical outcomes.

Abstract

We use the standard three-party Einstein-Podolsky-Rosen (EPR) setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities that may emerge in the EPR setting can change outcome of the game. Our setup requires that the quantum game attains classical interpretation for factorizable joint probabilities. We analyze the generalized three-player game of Prisoner's Dilemma (PD) and show that the players can indeed escape from the classical outcome of the game because of non-factorizable joint probabilities. This result for three-player PD contrasts strikingly with our earlier result for two-player PD for which even non-factorizable joint probabilities are not found to be helpful to escape from the classical outcome of the game.