Constructing quantum games from non-factorizable joint probabilities

TL;DR

This paper introduces a probabilistic framework linking classical and quantum games through EPR experiment probabilities, showing how non-factorizability influences Nash equilibria in various two-player games.

Contribution

It presents a novel approach to construct quantum games from EPR probabilities, highlighting how non-factorizability affects game outcomes and equilibria.

Findings

Non-factorizable probabilities do not help escape classical outcomes in Prisoner's Dilemma.

Certain non-factorizable probabilities lead to new Nash equilibria in Chicken game.

Framework unifies classical and quantum game analysis through joint probability structures.

Abstract

A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when joint probabilities are factorizable and a quantum game corresponds when these probabilities cannot be factorized. We analyze how non-factorizability changes Nash equilibria in two-player games while considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this framework we find that for the game of Prisoner's Dilemma even non-factorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the Chicken game, however, we find that the two non-factorizable sets of joint probabilities, that maximally violates the Clauser-Holt-Shimony-Horne (CHSH) sum of correlations, indeed result in new Nash equilibria.