Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

A Al-Khedhairi

doi:10.1155/2020/8903183

Abstract

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

Highlights

Many scientists have created diverse variations of Cournot oligopoly games
Peng et al [36] analyzed complex dynamics for Cournot-remanufacturing duopoly game based on bounded rationality
We investigate Cournot duopoly game based on fractional marginal profit

Summary

Introduction

Many scientists have created diverse variations of Cournot oligopoly games. Cournot duopoly game was the first oligopoly game [1]. Peng et al [36] analyzed complex dynamics for Cournot-remanufacturing duopoly game based on bounded rationality. Al-khedhairi [38] introduced a fractional-order Cournot triopoly game and discussed the effects of the memory on the dynamics of the game. Remanufacturing Cournot duopoly game based on a nonlinear utility function has been studied by Askar and Al-khedhairi [39]. We investigate Cournot duopoly game based on fractional marginal profit. E fractional-order marginal profit method presented here is a generalization of the classical one It thinks about the nearness of a memory of purchasers about the past costs of the generation. We will discuss the dynamics of the game (11)

Equilibrium and Stability

Numerical Simulation