Existence of equilibria in quantum Bertrand-Edgeworth duopoly game

TL;DR

This paper investigates the existence of Nash equilibria in classical and quantum versions of a duopoly game, revealing how quantum entanglement influences equilibrium convergence and addressing the Edgeworth paradox.

Contribution

It demonstrates that quantum entanglement causes the realistic duopoly model to converge to the idealized one, providing new insights into quantum game theory and economic equilibria.

Findings

Classical equilibria exist under stricter conditions in the realistic model.

Quantum entanglement causes the realistic model to converge to the idealized one.

The study addresses the Edgeworth paradox in a quantum context.

Abstract

Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.