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

Product cannibalisation is a well-known phenomenon in marketing and technological research and describes the case when a new product steals sales from another product under the same brand. A very special case of cannibalisation may occur when the older product react to the competitive strength of the newer one, absorbing the corresponding market shares. Given its special character, we call this phenomenon inverse product cannibalisation. We suppose that a case of inverse cannibalisation is observed between two products of Apple Inc., the iPhone and the more recent iPad, and the first has been able to succeed at the expense of the second. To explore this hypothesis, within a diffusion of innovations perspective, we propose a modified Lotka-Volterra model for mean trajectories in asymmetric competition, allowing us to test the presence and the extent of the inverse cannibalisation phenomenon. A SARMAX refinement integrates the short term predictions with seasonal and autodependent components. A non-dimensional representation of the proposed model shows that the penetration of the second technology has been beneficial for the first, both in terms of market size and life cycle length.