A fractional-order difference Cournot duopoly game with long memory

TL;DR

This paper introduces a fractional-order difference model for Cournot duopoly games incorporating long memory, analyzing stability, Nash equilibria, and chaos detection using fractional calculus and numerical methods.

Contribution

It develops a novel fractional-order discrete duopoly model that accounts for historical decision-making, extending classical game theory with long memory effects.

Findings

Nash equilibria are characterized within the fractional-order framework.

The model's stability depends on fractional order parameters.

Chaos can be detected using the 0-1 test algorithm.

Abstract

We reconsider the Cournot duopoly problem in light of the theory for long memory. We introduce the Caputo fractional-order difference calculus to classical duopoly theory to propose a fractional-order discrete Cournot duopoly game model, which allows participants to make decisions while making full use of their historical information. Then we discuss Nash equilibria and local stability by using linear approximation. Finally, we detect the chaos of the model by employing a 0-1 test algorithm.