Simulation of continuous variable quantum games without entanglement

TL;DR

This paper introduces a decoherence-free quantum simulation of Cournot's Duopoly that achieves a new Nash equilibrium without entanglement, analyzing effects of asymmetric information and photon loss, revealing phase transition-like behavior.

Contribution

It presents a novel entanglement-free quantum simulation scheme for Cournot's Duopoly with unique equilibrium properties and robustness against photon loss, expanding quantum game theory.

Findings

Existence of a new Nash equilibrium without entanglement

Decoherence-free against symmetric photon loss

Phase transition-like behavior in profits with asymmetry

Abstract

A simulation scheme of quantum version of Cournot's Duopoly is proposed, in which there is a new Nash equilibrium that may be also Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against the symmetric photon loss. Furthermore, we analyze the effects of the asymmetric information on this simulation scheme and investigate the case of asymmetric game caused by asymmetric photon loss. A second-order phase transition-like behavior of the average profits of the firm 1 and firm 2 in Nash equilibrium can be observed with the change of the degree of asymmetry of the information or the degree of "virtual cooperation". It is also found that asymmetric photon loss in this simulation scheme plays a similar role with the asymmetric entangled states in the quantum game. PACS numbers: 02.50.Le, 03.67.-a