基于异质阈值模型和平均场理论刻画了社会网络扩散,分析了邻居效应、阈值分布和网络度分布对扩散的影响。结果表明:邻居效应或阈值分布均值的减小将加速扩散及增大均衡状态值,阈值分布方差的减小将减缓初始扩散,且满足一定条件下,将加速扩散收尾过程;邻居效应较弱时,度分布异质性的增加将加速初始扩散,反之亦然;邻居效应和阈值分布满足一定条件时,扩散初始速度将呈现出超指数增长;邻居效应、阈值分布或度分布的变化均可使扩散均衡状态值发生跳跃式增长。
Based on heterogenous threshold model and mean-field theory, we analyse the impact of neighbor effect, threshold distribution and degree distribution on the diffusion process and equilibrium. The result shows that the decrease in neighbor effect or the mean of threshold distribution would speed up the diffusion process and increase the equilibrium value. Besides, the decrease in the variance of threshold distribution would slow down the initial diffusion process, and would also speed up the end-stage diffusion when some conditions are given; if the neighbor effect is low, the increase in the heterogeneity of degree distribution would speed up the initial diffusion stage; the initial diffusion would experience a super-exponential increase stage when a certain relationship between the neighbor effect and the threshold distribution is met; the change in neighbor effect, threshold distribution or degree distribution may lead to a jump increase of the equilibrium value.
[1] Boccaletti S, Latora V, Moreno Y, et al. Complex networks: structure and dynamics[J].Physics Reports, 2006, 424 (4/5): 175-308.
[2] Newman M E J. The structure and function of complex networks[J].SIAM Review, 2003, 45(2): 167-256.
[3] Centola D.The spread of Behavior in an online social network experiment[J].Science, 2010, 329: 1194-1197.
[4] 赵正龙, 陈忠, 孙武军, 等. 具有差异化选择特征的复杂社会网络扩散研究[J].管理科学学报, 2010, 13 (3): 38-48.
Zhao ZhengLong, Chen Zhong, Sun WuJun, et al. Diffusion with property of differential choice in complex social network[J].Journal of Management Sciences in China, 2010, 13(3):38-48.
[5] Duan W, Chen Z, Liu Z. Efficient target strategies for contagion in scale-free networks[J].Physical Review E, 2005, 72(2): 26-133.
[6] 段文奇, 陈忠. 网络效应新产品成功的关键: 产品质量还是安装基础? [J].系统工程理论与实践, 2007, 23(7): 144-148.
Duan WenQi, Chen Zhong. Key factor to drive success of new product with network effects: product quality or installed base? [J].System Engineering Theory&Practice, 2007, 23(7): 144-148.
[7] Choi H, Kim S H, Lee J. Role of network structure and network effects in diffusion of innovations[J].Industrial Marketing Management, 2010, 39(1): 170-177.
[8] Ohara K, Kazumi S, Masahiro K, et al. Effect of in/out degree correlation on influence degree of two contrasting in formation diffusion models[C].SBP 2012, LNCS 7227: 131-138.
[9] Lopez-Pintado D. Diffusion in complex social networks[J].Games and Economics Behavior, 2008, 62(2): 573-590.
[10] Valente T W. Social network thresholds in the diffusion of innovations[J].Social Networks, 1996, 18: 69-89.
[11] Young H P. Innovation diffusion in heterogeneous populations:contagion,social influence,and social learning[J].American Economic Review, 2009, 99(5): 1898-1924.
[12] Gleeson J P, Cahalane D J. Seed size strongly affects cascades on random networks[J].Physical review E, 2007, 75, 056103.
[13] Granovetter M. Threshold models of collective behavior[J].American Journal of Sociology, 1978, 83: 1420-1443.
[14] Granovetter M, Song R. Threshold models of interpersonal effects in consumer demand[J].Journal of Economic Behavior and Organization, 1986, 7: 83-89.
[15] Macy M W. Chains of cooperation:threshold effects in collective action[J].American Sociology Review, 1991, 56: 730-737.
[16] Lopez-Pintado D. Influence networks[J].Games and Economics Behavior, 2012, 75: 776-787.
[17] Pastor-Satorras R,Vespignani A. Epidemic dynamics and endemic states in complex networks[J].Physical Review Letters, 2000, 86(24): 3200-3203.
[18] Dodds P S, Watts D J. Universal behavior in a generalized model of contagion[J].Pyhsical Review Letters, 2004, 92(21), 218701.
[19] Jackson M O,Yariv L. Diffusion of behavior and equilibrium properties in network games[J].American Economic Review, 2007, 97(2): 92-98.
[20] Yann B. Anti-coordination and social interactions[J].Games and Economic Behavior, 2007, 58: 30-49.
