Cellular Automata with Network Incubation in Information Technology Diffusion

Innovation diffusion of network goods determines direct network externalities that exhibit delayed full benefits, depressing sales for long periods. We model a multiplicative dynamic market potential driven by a latent heterogeneous individual threshold derived from a basic economic theory by Economides and Himmelberg (1995) which is embedded in a special Cellular Automata representation. The corresponding mean field approximation of its aggregate version is a Riccati equation with a closed form solution. This allows the detection of a change–point time separating an incubation period from a subsequent take–off due to a sufficient critical mass acting as a collective threshold. Weighted nonlinear least squares methodology is the main inferential technique. An application is analysed with reference to USA fax machine diffusion.