Diffusion of new products with heterogeneous consumers

TL;DR

This paper investigates how consumer heterogeneity affects the speed of new product diffusion using a stochastic discrete Bass model, revealing complex effects depending on heterogeneity patterns and network structure.

Contribution

It provides a detailed analysis of how heterogeneity in external and internal influence rates impacts diffusion speed and dominance, including effects of network completeness and spatial distribution.

Findings

Heterogeneity in only one influence type slows diffusion.

Heterogeneity in both influence types can either slow or accelerate diffusion.

Network structure and heterogeneity distribution critically affect diffusion dynamics.

Abstract

Does a new product spread faster among heterogeneous or homogeneous consumers? We analyze this question using the stochastic discrete Bass model, in which consumers may differ in their individual external influence rates $\{p_j \}$ and in their individual internal influence rates $\{ q_j \}$. When the network is complete and the heterogeneity is only manifested in $\{p_j \}$ or only in $\{ q_j \}$, it always slows down the diffusion, compared to the corresponding homogeneous network. When, however, consumers are heterogeneous in both $\{p_j\}$ and $\{q_{j}\}$, heterogeneity slows down the diffusion in some cases, but accelerates it in others. Moreover, the dominance between the heterogeneous and homogeneous adoption levels is global in time in some cases, but changes with time in others. Perhaps surprisingly, global dominance between two networks is not always preserved under "additive transformations", such as adding an identical node to both networks. When the network is not complete, the effect of heterogeneity depends also on its spatial distribution within the network.