Reinforcement-Driven Spread of Innovations and Fads
Abstract
We propose kinetic models for the spread of permanent innovations and transient fads by the mechanism of social reinforcement. Each individual can be in one of M+1 states of awareness 0,1,2,...,M, with state M corresponding to adopting an innovation. An individual with awareness k<M increases to k+1 by interacting with an adopter. Starting with a single adopter, the time for an initially unaware population of size N to adopt a permanent innovation grows as ln(N) for M=1, and as N^{1-1/M} for M>1. The fraction of the population that remains clueless about a transient fad after it has come and gone changes discontinuously as a function of the fad abandonment rate lambda for M>1. The fad dies out completely in a time that varies non-monotonically with lambda.
Cite
@article{arxiv.1104.4107,
title = {Reinforcement-Driven Spread of Innovations and Fads},
author = {P. L. Krapivsky and S. Redner and D. Volovik},
journal= {arXiv preprint arXiv:1104.4107},
year = {2015}
}
Comments
4 pages, 2 columns, 5 figures, revtex 4-1 format; revised version has been expanded and put into iop format, with one figure added