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Volume 2018, Article ID 9649863, 13 pages
Research Article

The Evolution of Price Competition Game on Complex Networks

1School of Modern Posts, Xi’an University of Posts and Telecommunications, Xi’an, ShaanXi, China
2Industrial Economics Research Institute, Xi’an University of Posts and Telecommunications, Xi’an, ShaanXi, China
3Department of Mechanical and Materials Engineering, College of Engineering & Applied Science, University of Cincinnati, Cincinnati, OH, USA

Correspondence should be addressed to Jing Shi;

Received 29 November 2017; Revised 22 April 2018; Accepted 12 May 2018; Published 9 July 2018

Academic Editor: Shahadat Uddin

Copyright © 2018 Feng Jie Xie and Jing Shi. 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.


The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.