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Product cannibalisation is a well-known phenomenon in marketing andtechnological research and describes the case when a new product steals salesfrom another product under the same brand. A very special case ofcannibalisation may occur when the older product react to the competitivestrength of the newer one, absorbing the corresponding market shares. Given itsspecial character, we call this phenomenon inverse product cannibalisation. Wesuppose that a case of inverse cannibalisation is observed between two productsof Apple Inc., the iPhone and the more recent iPad, and the first has been ableto succeed at the expense of the second. To explore this hypothesis, within adiffusion of innovations perspective, we propose a modified Lotka-Volterramodel for mean trajectories in asymmetric competition, allowing us to test thepresence and the extent of the inverse cannibalisation phenomenon. A SARMAXrefinement integrates the short term predictions with seasonal andautodependent components. A non-dimensional representation of the proposedmodel shows that the penetration of the second technology has been beneficialfor the first, both in terms of market size and life cycle length.

On inverse product cannibalisation: a new Lotka-Volterra model for asymmetric competition in the ICTs