Diffusion of new products on networks
Abstract: Diffusion of new products is a classical problem in Marketing, where it has been extensively studied using compartmental Bass models. These compartmental models implicitly assume that all individuals are homogeneous and connected to each other. To relax these assumptions, one can go back to the more fundamental discrete Bass models on networks, which are stochastic particle models for the adoption state of each individual. These models may look "similar" to discrete epidemiological models on networks, but are fundamentally different.
In this talk, I will present the emerging mathematical theory for the discrete Bass model, with a special focus on the diffusion of residential solar systems, and review some analytical tools developed for this model (indifference principle, funnel-node theorems, ….). The main focus of the talk will be the effects on the aggregate diffusion of the network structure (complete, Cartesian, random, percolation, boundary effects, …), of heterogeneity (qualitative, quantitative), and of recovery (Bass-SIR model).
Bio: Gadi Fibich is a professor of Applied Mathematics at Tel Aviv University. In recent years, his research focuses on mathematical modeling in marketing, economics, and epidemiology.