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

23 Pages Posted: 28 Aug 2010

See all articles by Gadi Fibich

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences

Ro'i Gibori

Tel Aviv University - School of Mathematical Sciences

Eitan Muller

New York University (NYU) - Department of Marketing; Interdisciplinary Center (IDC) Herzliyah

Date Written: May 30, 2010

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

Suggested Citation

Fibich, Gadi and Gibori, Ro'i and Muller, Eitan, A Comparison of Stochastic Cellular Automata Diffusion with the Bass Diffusion Model (May 30, 2010). NYU Stern School of Business, Available at SSRN: https://ssrn.com/abstract=1663544 or http://dx.doi.org/10.2139/ssrn.1663544

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Ro'i Gibori (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Eitan Muller

New York University (NYU) - Department of Marketing ( email )

Henry Kaufman Ctr
44 W 4 St.
New York, NY
United States

Interdisciplinary Center (IDC) Herzliyah ( email )

P.O. Box 167
Herzliya, 46150
Israel

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