Competition Modelling in Multi-Innovation Diffusions. Part II: Unbalanced Models.

Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest for involved firms. In the companion article, we studied balanced models that are adequate to describe a homogeneous category for which within-brand and cross-brand word-of-mouth effects are indistinguishable. Conversely, in this paper we propose an unbalanced model that, besides separating these two imitative sources, also allows for a change in the parameter values of the first entrant as soon as the second one enters the market. We prove that our model has a closedform solution allowing parameters to be estimated with sales data. Moreover, we compare our model with other unbalanced models, both from a theoretical point of view and from an empirical one, by comparing their performance on pharmaceutical drug data.