Phase-transition-like Behavior of Quantum Games

TL;DR

This paper explores phase-transition-like phenomena in quantum games, especially the generalized Prisoners' Dilemma, revealing how quantum properties can cause abrupt changes in game outcomes depending on entanglement levels.

Contribution

It introduces a method to analyze the origin of phase-transition-like behavior in quantum games and demonstrates its application to the generalized Prisoners' Dilemma.

Findings

Quantum games show phase-transition-like behavior depending on entanglement.

Different payoff settings lead to varied phase-transition phenomena.

Classical game behavior remains unchanged despite quantum phase transitions.

Abstract

The discontinuous dependence of the properties of a quantum game on its entanglement has been shown up to be very much like phase transitions viewed in the entanglement-payoff diagram [J. Du et al., Phys. Rev. Lett, 88, 137902 (2002)]. In this paper we investigate such phase-transition-like behavior of quantum games, by suggesting a method which would help to illuminate the origin of such kind of behavior. For the particular case of the generalized Prisoners' Dilemma, we find that, for different settings of the numerical values in the payoff table, even though the classical game behaves the same, the quantum game exhibits different and interesting phase-transition-like behavior.