MVSU professor Dr. Xiaoqin P. Wu and student Travis Dixon have co-authored a research paper titled “Bifurcation Analysis of a Model of Cournot Duopoly with Delays”, which has been accepted for publication by the Pacific Journal of Applied Mathematics.
Duopoly is a game of competition and reaction between two companies which have dominant influence and control over a market. Each company produces the same product and does not cooperate with its rival. In order to maximize the profit, each company takes action based on the reaction from its rival to compete with its rival.
According to Dr. Wu, the first mathematical model of duopoly games was given by the French economist Cournot in 1838 who described the competition of two companies on quantities of their products. Cournot duopoly games are very complicated even from the view of point of mathematical analysis since each company takes different action and the reaction from its rival is also different.
“In this research, a delayed duopoly game is considered since companies need time to take action against their competitors,” said Wu. “The dynamical behaviors of Cournot duopoly games are complicated and in some situations they are chaotic and cannot be predicted. In this research, oscillations or limit cycles had been studied since they represent cyclic behaviors of quantities which are very important in Mathematics and Economics.”
This project was designed for students in the Department of Mathematics and Computer Science (MCIS) to apply their skills in real-world applications. “This project supports an effort to increase faculty/student research collaboration. We hope that our research may shed some light on the complicated economic phenomenon and that one may be able to use it in day to day business practices and in predicting the future behaviors of two companies,” said Wu.
The research was funded by NIFA/USDA Promoting Research Project and the MVSU Office of Title III, aimed to expose students to the faculty research and to fill the gap between mathematical theories and applications in an effort for students to apply their knowledge of mathematics and computer skills to other fields such as economics and engineering.