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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 809795, 5 pages
Research Article

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

1Department of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 8 September 2013; Revised 24 October 2013; Accepted 24 October 2013

Academic Editor: Pu-yan Nie

Copyright © 2013 S. S. Askar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.