Fashion and Homophily∗

Fashion, as a “second nature” to human being, plays a quite non-trivial role not only in economy but also in many other areas of our society, including education, politics, arts, and even academics. We investigate fashion through a network game model, which is referred to as the fashion game, where there are two types of agents, conformists and rebels, who are allocated on a network. Each agent has two actions to choose, and interacts only with her neighbors. Conformists prefer to match the majority action among her neighbors while rebels like to mismatch. Theoretically, the fashion game is a network extension of three elementary games, namely coordination game, anti-coordination game, and matching pennies. We are especially interested in how social interaction structures affect the evolution of fashion. The conclusion is quite clean: homophily, in general, inhibits the emergence of fashion cycles. To establish this, two techniques are applied, i.e. the best response dynamics and a novel partial potential analysis. ∗This is a sister working paper with: Zhi-gang Cao, Cheng-zhong Qin, Xiao-guang Yang, Bo-yu Zhang, A heterogeneous network game perspective of fashion cycle. The research is supported by the 973 Program (2010CB731405) and National Natural Science Foundation of China (71101140). We gratefully acknowledge helpful comments from Xujin Chen, Zhiwei Cui, Xiaodong Hu, Weidong Ma, Changjun Wang, Lin Zhao, and Wei Zhu. †Department of Mathematics, Beijing Normal University, Beijing, 100875, China. Email: [email protected]. ‡MADIS, 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]. ¶MADIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected].