Uniqueness of Nash equilibria in quantum Cournot duopoly game

TL;DR

This paper investigates how quantum entanglement influences Nash equilibria in a Cournot duopoly, showing that strong entanglement can eliminate multiple equilibria and lead to more optimal outcomes.

Contribution

It demonstrates that quantum entanglement can remove multiplicity of Nash equilibria in a Cournot game, aligning equilibrium outcomes closer to the social optimum.

Findings

High entanglement reduces equilibrium multiplicity.

Stronger entanglement leads to more optimal equilibria.

Quantum strategies improve efficiency over classical counterparts.

Abstract

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.