Noise effects in a three-player Prisoner's Dilemma quantum game

TL;DR

This paper investigates how decoherence and correlated noise influence a three-player quantum Prisoner's Dilemma game, revealing that quantum advantages persist under certain noise conditions and that correlated noise affects payoff reductions.

Contribution

It demonstrates that the Nash equilibrium remains unchanged with correlated noise and that quantum players outperform classical ones despite noise effects, extending previous two-player results.

Findings

Quantum players outperform classical players under noise.

Nash equilibrium remains stable with correlated noise.

Payoff reduction is controlled by correlated noise.

Abstract

We study the three-player Prisoner's Dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off over the classical players. It is also seen that the game's Nash equilibrium does not change in the presence of correlated noise in contradiction to the effect of decoherence in multiplayer case. Furthermore, it is shown that for maximum correlation the game does not behave as a noiseless game and the quantum player is still better off for all values of the decoherence parameter p which is not possible in the two-player case. In addition, the payoffs reduction due to decoherence is controlled by the correlated noise throughout the course of the game.