Unstable diffusion in social networks

How and to what extent will new activities spread through social ties? To answer this question, we present an analytical framework that allows us to describe the diffusion dynamics on complex networks more accurately than the conventional mean-field approach. Based on two classes of network games, we find that the spread of multiple activities is expressed as a saddle path, and thus, inherently unstable. In particular, when the two activities are sufficiently substitutable, either of them will dominate the other by chance even if they are equally attractive ex ante. We argue that, in environments where such symmetry-breaking occurs, any average-based approximation method may not correctly capture the Nash equilibrium — the steady state of an actual diffusion process.