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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 251702, 11 pages
http://dx.doi.org/10.1155/2013/251702
Research Article

Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality

1School of Management, Tianjin University, Tianjin 300072, China
2College of Science, Tianjin University of Science and Technology, Tianjin 300457, China

Received 18 June 2013; Accepted 19 August 2013

Academic Editor: Massimiliano Ferrara

Copyright © 2013 Junhai Ma and Hongwu Wang. 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.

Abstract

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.