Market potential dynamics and diffusion of innovation: modelling synergy between two driving forces

The presence of a slowdown in new products' life cycle has recently received notable attention by many innovation diffusion scholars, that have tried to explain and model it on a typical dual-market hypothesis [1-6]. This discrete unnecessary taxonomy has been overcome in the co-evolutionary model by Guseo and Guidolin [7], that includes a latent market potential based on a dynamic network. The model is obtained through Cellular Automata whose aggregate mean-field approximation, is expressed by a non-autonomous Riccati Equation with exogenous interventions, extending previous results [8]. Its closed form solution is flexible. In this paper we propose an alternative explanation of the slowdown pattern, derived from a density decomposition of diffusion that presents an interpretable synergy between two driving forces: communication and adoption. We test the model on weekly sales data of six pharmaceutical drugs exhibiting a slowdown in their life cycle and observe that this is always identified almost perfectly by the model. A deeper analysis of the interaction between communication and adoption, based on the likelihood ratio order or the usual stochastic order (see e.g. [9]) shows that location indexes of each component (communication and adoption), can inform on which of the two had a driving role in early diffusion. Contrary to a general expectation according to which communication should precede adoptions, our findings show that in two cases adoptions were the main driver in early life cycle. We argue that this behaviour may be due to the nature of the drug considered: new drugs developed for severe pathologies will be likely to have an accumulated demand at the time of launch, while drugs for minor ailments will present a normal behaviour, ''first communication, then adoption''. [1] G. Moore, Crossing the Chasm: Marketing and selling technology products to mainstream customers, Harper Collins P., New York, 1991. [2] J. Goldenberg, B. Libai, E. Muller, Riding the Saddle: How Cross-Market Communications Can Create a Major Slump in Sales, J. of Marketing 66(2), (2002) 1-16. [3] E. Muller, G. Yogev, When does the majority become majority? Empirical analysis of the time at which main market adopters purchase the bulk of our sales, Technological Forecasting and Social Change 73(9), (2006) 1107-1120. [4] Karmeshu, D. Goswami, Stochastic evolution of innovation diffusion in heterogeneous groups: study of life cycle patterns, IMA Journal of Management Mathematics 12, (2001) 107-126. [5] D. Vakratsas, C. Kolsarici, A dual-market diffusion model for a new prescription pharmaceutical, Intern. J. of Research in Marketing 25, (2008) 282-293. [6] C. Van den Bulte, Y.V. Joshi, New Product Diffusion with Influentials and Imitators, Marketing Science 26(3), (2007) 400-421. [7] R. Guseo, M. Guidolin, Modelling a dynamic market potential: A class of automata networks for diffusion of innovations, Technological Forecasting and Social Change (Forthcoming). [8] R. Guseo, A. Dalla Valle, M. Guidolin, World Oil Depletion Models: Price Effects Compared with Strategic or Technological Interventions,Technological Forecasting and Social Change 74(4), (2007) 452-469. [9] A. Mueller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, Wiley, New York, 2002