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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 2363804, 12 pages
Research Article

Dynamics of a Duopoly Game with Two Different Delay Structures

Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Shumin Jiang

Received 23 March 2017; Revised 8 May 2017; Accepted 14 May 2017; Published 13 June 2017

Academic Editor: Douglas R. Anderson

Copyright © 2017 Shumin Jiang 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.


Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.