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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 698270, 13 pages
http://dx.doi.org/10.1155/2012/698270
Research Article

Complexity of a Duopoly Game in the Electricity Market with Delayed Bounded Rationality

College of Management and Economics, Tianjin University, Tianjin 300072, China

Received 2 May 2012; Accepted 21 November 2012

Academic Editor: Mingshu Peng

Copyright © 2012 Junhai Ma and Hongliang Tu. 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

According to a triopoly game model in the electricity market with bounded rational players, a new Cournot duopoly game model with delayed bounded rationality is established. The model is closer to the reality of the electricity market and worth spreading in oligopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Its complex dynamics is demonstrated by means of the largest Lyapunov exponent, bifurcation diagrams, phase portraits, and fractal dimensions. Since the output adjustment speed parameters are varied, the stability of Nash equilibrium gives rise to complex dynamics such as cycles of higher order and chaos. Furthermore, by using the straight-line stabilization method, the chaos can be eliminated. This paper has an important theoretical and practical significance to the electricity market under the background of developing new energy.