The Dynamics of Book Sales: Endogenous versus Exogenous Shocks in Complex Networks

Abstract

We present an extensive study of the foreshock and aftershock signatures accompanying peaks of book sales. The time series of book sales are derived from the ranking system of Amazon.com. We present two independent ways of classifying peaks, one based on the acceleration pattern of sales and the other based on the exponent of the relaxation. They are found to be consistent and reveal the co-existence of two types of sales peaks: exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous sale peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks. We develop a simple epidemic model of buyers connected within a network of acquaintances which propagates rumors and opinions on books. The comparison between the predictions of the model and the empirical data confirms the validity of the model and suggests in addition that social networks have evolved to converge very close to criticality (here in the sense of critical branching processes of opinion spreading). We test in details the evidence for a power law distribution of book sales and confirm a previous indirect study suggesting that the fraction of books (density distribution) $P(S)$ of sales S is a power law P(S) ~ 1/S^{1+mu} with mu close to 2. A short version of this work appeared in Sornette, D. et al., Phys. Rev. Letts. 93 (22), 228701 (2004).