Endo- vs. exogenous shocks and relaxation rates in book and music “sales”

In this paper, we analyse the response of music and book sales to an external field and a buyer herding. We distinguish endogenous and exogenous shocks. We focus on some case studies, whose data have been collected from ranking on amazon.com. We show that an ensemble of equivalent systems quantitatively respond in a same way to a similar “external shock”, indicating roads to universality features. In contrast to Sornette et al. [Phys. Rev. Lett. 93 (2004) 228701] who seemed to find power-law behaviours, in particular at long times, a law interpreted in terms of an epidemic activity, we observe that the relaxation process can be as well seen as an exponential one that saturates toward an asymptotic state, itself different from the pre-shock state. By studying an ensemble of 111 shocks, on books or records, we show that exogenous and endogenous shocks are discriminated by their short-time behaviour: the relaxation time seems to be twice shorter in endogenous shocks than in exogenous ones. We interpret the finding through a simple thermodynamic model with a dissipative force.