Unstable diffusion in social networks

TL;DR

This paper presents a new framework for modeling the complex and potentially unstable diffusion of multiple activities in social networks, highlighting how substitutability can lead to unpredictable dominance and challenge traditional equilibrium calculations.

Contribution

It introduces a sophisticated model that captures the instability and saddle-path dynamics of multi-activity diffusion on complex networks, surpassing standard mean-field approaches.

Findings

Diffusion follows a saddle path and can be highly unstable.

Substitutable activities may lead to dominance by chance.

Average-based methods fail to predict the true steady state.

Abstract

How and to what extent will new activities spread through social ties? Here, we develop a more sophisticated framework than the standard mean-field approach to describe the diffusion dynamics of multiple activities on complex networks. We show that the diffusion of multiple activities follows a saddle path and can be highly unstable. In particular, when the two activities are sufficiently substitutable, either of them would dominate the other by chance even if they are equally attractive ex ante. When such symmetry-breaking occurs, any average-based approach cannot correctly calculate the Nash equilibrium - the steady state of an actual diffusion process.