Sequential market entries and competition modelling in multi-innovation diffusions

The diffusion of innovations for simultaneous processes cannot take into account and properly explain systematic perturbations due to competition-substitution effects if they are examined one by one. A first aspect in simultaneous competing diffusions is the distinction between simultaneous market entries (synchronic competition) and sequential entries (diachronic competition). In the latter case, the beginning of competition may upset the first entrant’s diffusion. A second important aspect in multiple competition is represented by the choice to model the word-of-mouth effect either at the category level (balanced model) or at the brand level, separating the within-brand effect from the cross-brand one (unbalanced model). In this paper, balanced models are studied, and we propose a model that allows for a change in the parameter values of the first entrant as soon as the second one enters the market. The resulting differential system has a closed-form solution that enables, through sales data, an empirical validation of the assumptions underlying the model structure, improving the forecasting accuracy. An application to pharmaceutical drug competition is discussed.