yväskylä, Finland e-mail: Lauri.Frank@jyu.fr P. Tyrväinen and O. Mazhelis (eds.), Vertical Software Industry Evolution, Contributions to Management Science, DOI 10.1007/978-3-7908-2352-3_3, C Springer-Verlag Berlin Heidelberg 2009 L. Frank Quantitative modeling of the time path of an innovation's diffusion has been traced back to the early 1940s: In their study, Ryan and Gross (1943) used the cumulative normal curve to explain the sigmoid shape of the diffusion of hybrid corn. In later studies, Griliches (1957) and Mansfield (1961) implemented analogies from theories of epidemiological disease spread on innovation diffusion models. Following this idea, information about an innovation would spread like a disease, by contagion from one carrier to another. Thus the diffusion of that innovation would reach a sigmoid shape on the macro level: In the beginning the diffusion would be slow, in the mid-phase fast, and in the end slow again (see Fig. 1). These three phases were named by Griliches (1957) as the origin, diffusion and saturation phases - but they are also commonly known as the innovation, growth and maturity phases. Because of the analogy to the spread of diseases, these models are also known as "epidemic" diffusion models. Mathematically the epidemic theory is in line with the logistic growth model developed by P.-F. van Verhulst in 1848 for modeling population growth. The logistic model has been successfully applied in several technology diffusion stud- ies, for example to the diffusion of mobile communications (e.g., Gruber and Verboven 2001a; Frank 2004). Instead of deriving the logistic model from the epidemic theory, it may also be derived from network effects, or from a demand function (see Wang 2006). In marketing, it is common to use the Bass (1969) diffusion model, which considers epidemic diffusion caused by "internal influence" (information exchange between adopters), and adds "external influence" (information from external sources) to it. As mentioned above, several alternatives to the idea of pa