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Abstract and Applied Analysis
Volume 2013, Article ID 406743, 10 pages
Research Article

New Analyses of Duopoly Game with Output Lower Limiters

1School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
2School of Management, Jiangsu University, Zhenjiang 212013, China
3Computational Experiment Center for Social Science, Jiangsu University, Zhenjiang 212013, China
4Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Received 23 October 2012; Accepted 30 December 2012

Academic Editor: Chuandong Li

Copyright © 2013 Zhaohan Sheng et al. 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.


In the real business world, player sometimes would offer a limiter to their output due to capacity constraints, financial constraints, or cautious response to uncertainty in the world. In this paper, we modify a duopoly game with bounded rationality by imposing lower limiters on output. Within our model, we analyze how lower limiters have an effect on dynamics of output and give proof in theory why adding lower limiters can suppress chaos. We also explore the numbers of the equilibrium points and the distribution of conditioned equilibrium points. Stable region of the conditioned equilibrium is discussed. Numerical experiments show that the output evolution system having lower limiters becomes more robust than without them, and chaos disappears if the lower limiters are big enough. The local or global stability of the conditional equilibrium points provides a theoretical basis for the limiter control method of chaos in economic systems.