Quantum Model of Bertrand Duopoly

TL;DR

This paper introduces a quantum version of the Bertrand duopoly game, demonstrating how entanglement influences firms' profits and resolves classical dilemmas by providing higher payoffs at equilibrium.

Contribution

It presents a novel quantum model of Bertrand duopoly and analyzes how entanglement affects equilibrium and payoffs, resolving classical game dilemmas.

Findings

Maximally entangled states yield a unique Nash equilibrium.

Quantum entanglement increases firms' payoffs compared to classical game.

Entanglement resolves the classical dilemma in Bertrand duopoly.

Abstract

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entanglement in the initial state gives payoffs higher to the firms than the classical payoffs at the Nash equilibrium. As a result the dilemma like situation in the classical game is resolved.