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A MODEL OF THE DIFFUSION OF BREAKTHROUGH PRODUCTS

Breakthrough products are innovative products that address a new set of needs and thus require the creation of a new market in order to succeed. Due to this requirement, the eventual success of breakthrough products is notoriously difficult to predict. In this paper, a new model for the diffusion of breakthrough products is developed, based on the well-researched and widely accepted observation that new adopters need an acceptable reference before they actually adopt. This simple observation implies a reference network between potential adopters that can be modeled as a directed graph. If the reference network is assumed to be a random graph, a first order differential equation can be derived. The solution of the differential equation predicts initial exponential growth, followed by a stage when new adoption gradually declines as saturation sets in, similar in form to qualitative adoption life cycles. The model requires only a small number of parameters. The model assumes random networks but it is unlikely that many reference networks would be truly random graphs. Reference networks are examples of social networks and studies indicate that social networks typically are scale-free networks. Scale-free networks contain a few nodes with a very large number of incoming links, which means that a few reference sites are very widely acceptable. These special nodes are known as hubs in network terminology. Closed form expressions for diffusion in scale-free networks are more difficult to obtain but computer simulation demonstrates a number of important observations. The major observations are that the shape of the adoption curve is very similar for random and scale-free networks but that adoption by a reference hub in a scale-free network is both necessary and sufficient for the rapid diffusion of a breakthrough product.