Remarks on quantum duopoly schemes

TL;DR

This paper compares two quantum schemes for duopoly problems, analyzes their conditions for classical correspondence, and proposes refinements and a new quantum computational scheme for Cournot's duopoly.

Contribution

It provides a detailed comparison of quantum duopoly schemes, suggests necessary refinements, and introduces a new quantum computational approach for Cournot's duopoly.

Findings

Current quantum schemes need refinement to recover classical games

Refinements alter the analysis of Nash equilibria in quantum games

A new quantum computational scheme for Cournot's duopoly is proposed

Abstract

The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable that the other one. Using the Cournot's duopoly example we show that the current quantum schemes require a slight refinement so that they output the classical game in a particular case. Then we show how the amendment changes the way of studying the quantum games with respect to Nash equilibria. Finally, we define another scheme for the Cournot's duopoly in terms of quantum computation.