Quantum Cournot equilibrium for the Hotelling-Smithies model of product choice

TL;DR

This paper introduces a quantum approach to the spatial Cournot duopoly model, enabling continuous strategies and revealing that quantum entanglement leads to higher profits and larger strategic spaces at equilibrium.

Contribution

It presents the first quantization of the Hotelling-Smithies model, showing how quantum strategies expand strategic options and improve firm profits in spatial competition.

Findings

Quantum entanglement determines equilibrium for all location choices.

Firms achieve higher profits at quantum Nash equilibrium.

Quantum strategies enlarge the strategic space available to firms.

Abstract

This paper demonstrates the quantization of a spatial Cournot duopoly model with product choice, a two stage game focusing on non-cooperation in locations and quantities. With quantization, the players can access a continuous set of strategies, using continuous variable quantum mechanical approach. The presence of quantum entanglement in the initial state identifies a quantity equilibrium for every location pair choice with any transport cost. Also higher profit is obtained by the firms at Nash equilibrium. Adoption of quantum strategies rewards us by the existence of a larger quantum strategic space at equilibrium.