An analysis of a model for the diffusion of engineering innovations under multi-firm competition

We present a theoretical and experimental analysis of the model for diffusion of engineering innovations that has recently been proposed by Cao and Yang (2012). In particular, under a very mild and realistic assumption on the innovation coefficients, we show that a unique solution defined on the whole set of (positive) times does always exist. Moreover, a numerical method to solve the model by Cao and Yang is developed whose convergence is proven theoretically and which is shown by direct simulation to be very accurate and fast. Finally, an experimental assessment of the model is performed by considering the case of the US satellite radio market. Such an analysis highlights that the model by Cao and Yang can be very useful to predict the dynamics of the firms already present in the market as well the time evolution of new start-ups. Copyright