Reinforcement-Driven Spread of Innovations and Fads

TL;DR

This paper introduces kinetic models to describe how innovations and fads spread through social reinforcement, analyzing the dynamics of awareness and adoption over time in populations.

Contribution

It presents a novel kinetic modeling framework that captures the effects of social reinforcement on the spread of innovations and fads, including transient and permanent adoption behaviors.

Findings

Time to adoption scales as ln(N) for M=1 and as N^{1-1/M} for M>1.

Fraction of unaware individuals drops discontinuously with fad abandonment rate.

Fad extinction time varies non-monotonically with abandonment rate.

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.