A Comparison of Stochastic Cellular Automata Diffusion with the Bass Diffusion Model

Abstract

Diffusion of new products is an important problem in marketing research. One of the most prominent models in diffusion theory is the Bass Diffusion model that describes the number of adopters of new products as a differential equation. More recently, diffusion of products has been studied using agent-based modeling and in particular, stochastic cellular automata models. In this study we explore the relation between the Bass model and the cellular automata models. In particular, we explore the differences between the two models that are due to the fact that time is continuous in the Bass model but discrete in cellular automata models, and describe the conditions under which the cellular automata models converge to the Bass model. Empirical consequences are also discussed.

Keywords: Marketing, Diffusion, Cellular Automata, Stochastic Models, Nonspatial Models