A Heterogeneous Network Game Perspective of Fashion Cycle

Fashion, as a “second nature” of human being, has great economic impacts. In this paper, we apply a heterogenous network game to analyze the existence of a fashion cycle. There are two types of agents in the network game, conformists and rebels. Conformists prefer to match the action taken by the majority of her neighbors while rebels like to mismatch. Our results imply that social interaction structures play a crucial role in the evolution of fashion, especially the emergence of fashion cycles. For example, with a social network composed of a line or a ring, fashion will almost always evolve into a steady state where no flux is possible and thus can be deemed as disappeared. When the network is a star, however, for approximately half of all the configurations of agents’ types, a fashion cycle of length 4 will always emerge, regardless of the initial action profiles. ∗This is a sister working paper with: Bo-yu Zhang, Zhi-gang Cao, Cheng-zhong Qin, Xiao-guang Yang, Fashion and Homophily (April 14, 2013). Available at SSRN: http://ssrn.com/abstract=2250898 or http://dx.doi.org/10.2139/ssrn.2250898. The research of the first and third authors are supported by the 973 Program (2010CB731405) and National Natural Science Foundation of China (71101140). We gratefully acknowledge helpful discussions with Xujin Chen, Zhiwei Cui, Xiaodong Hu, Weidong Ma, Changjun Wang, Lin Zhao, and Wei Zhu. †Key Laboratory of Management, Decision & Information Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected]. ‡Department of Economics, University of California, Santa Barbara, CA 93106, USA. Email: [email protected]. §Key Laboratory of Management, Decision & Information Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected]. ¶Department of Mathematics, Beijing Normal University, Beijing, 100875, China. Email: [email protected].