The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

S S Askar

doi:10.1155/2013/809795

Abstract

It is reported in the literature that the most fundamental idea to address uncertainty is to begin by condensing random variables. In this paper, we propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points. A random cost function is introduced in this model. Each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multiobjective optimization problem, the expectation and worst-case approaches are used. A model of two rational firms that are in competition and produce homogenous commodities is introduced using an unknown demand function. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation, and chaos are investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation.

Highlights

In economic markets, competed firms often face considerable uncertainty upon their productions
We propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points
This uncertainty may be concerned with information on the exact demand function, rivals’ costs, or even components of firms own production cost

Summary

Introduction

In economic markets, competed firms often face considerable uncertainty upon their productions. Several studies concerning duopolistic models under uncertainty have investigated that in such models each firm is in risk neutral and may share or exchange its information on market uncertainty with its rival [5,6,7,8,9,10,11] In these studies, it has been investigated how market uncertainty with either unknown market demand or unknown constant marginal cost can affect firms’ behavior. It is assumed that the cost function used in this model is generated based on a random variable with zero mean and standard deviation equal to one.

Basic Concepts

Model and Main Results

Conclusions