Competition Modelling in Multi-Innovation Diffusions. Part I: Balanced Models

Diffusion of innovations within simultaneous processes examined as univariate models of separate trajectories cannot take into account and properly explain systematic perturbations due to competition-substitution effects. This inability is quite evident in special product categories such as pharmaceutical drugs based upon equivalent or similar active compounds. A second relevant 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 within-brand effect from cross-brand one (unbalanced model). The choice has to be grounded on the features of the products to be described. In this paper, balanced models will be studied, while the companion article is devoted to unbalanced ones. A third relevant aspect in simultaneous competing diffusions is the separation between synchronic and diachronic market entries. In the latter case, the proposed model is further extended in order to detect whether the beginning of competition alters the first entrant's diffusion parameters. The resulting differential system has a closed-form solution that allows an empirical validation through sales data of the assumptions underlying the model structure. An application to pharmaceutical drugs competition is discussed. Finally, we approach here the topic of agent heterogeneity by introducing a multivariate Cellular Automata representation which allows a feasible description of Complex Systems of this type with a direct specification of substitution effect between competing product