Cluster-based diffusion: Aggregate and disaggregate level modeling

Abstract

In this paper, we present a modeling approach for aggregate and disaggregate level models for cluster based diffusion of a new technology. For a homogenous population, the Bass (1969) model has been used extensively to predict the sales of newly introduced consumer durables. In comparison, little attention has been given to the modeling of the technology adoption by the industrial units present in disparate groups, called clusters. We study the pattern of diffusion of a new technology in a representative two-cluster situation. In the aggregate level modeling, we develop a model in which potential adopters of both clusters learn about the new technology from each other. Then, to focus on relatively micro-level phenomena, such as different propensities of imitation and innovation of firms within a cluster, we propose an agent based disaggregate model for cluster based diffusion of technology. In these disaggregate models, we capture the effects of heterogeneity and the inter-cluster and intra-cluster distances between the agents. Our results highlight two major points: (i) both aggregate and disaggregate models are in agreement with each other in terms of their patterns, and (ii) both of the models exhibit a form which is consistent with the Bass model. Thus, consistent with the general theme of "why the Bass model fits without decision variables" (Bass, Krishnan and Jain 1994), we find that the Bass model, when extended appropriately, can be expected to work well in the cluster based technology diffusion situation also. This modeling approach can also be applied in the related contexts such as diffusion of practices (e.g., Quality certifications) within a multi-divisional organization or across various networked clusters.