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A percolation model of the product lifecycle

Gerald P. Silverberg 1Koen Frenken Marco Valente 

1. IIASA, Schlossplatz 1, Wien 2261, Austria

Abstract

The product lifecycle model can be understood as a three-stage model of technological development associated with a particular product technology. In the explorative stage many different designs are developed, in the development stage products become standardized into a dominant design and in the mature stage only incremental changes occur within the dominant design. Though the product lifecycle model is widely shared and often applied in empirical research, innovation scholars have failed to develop systematic theoretical models that explain the different stages of technological development along the lifecycle. In this study, an attempt is made to contribute to the product lifecycle theory by developing a theoretical model based on percolation dynamics. The model combines the concept of increasing returns to adoption with information diffusion among heterogeneous consumers within social networks. Increasing returns are assumed to follow a power law in the total number of adopters. Consumers decide whether to adopt once a neighbour has adopted by using a threshold value for the price-performance index of the good drawn from a lognormal distribution. Consumers adopt variants of the good adopted by their neighbours near to the archetype in a topological product space. The main contribution of the model is that it replicates the three stages of the product lifecycle as an outcome of a single elementary process. The model also replicates the S-shaped diffusion curve and the occurrence of an industry shakeout.

 

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Related papers

Presentation: Oral at International Conference on Economic Science with Heterogeneous Interacting Agents 2008, by Gerald P. Silverberg
See On-line Journal of International Conference on Economic Science with Heterogeneous Interacting Agents 2008

Submitted: 2008-03-13 11:56
Revised:   2009-06-07 00:48