Has the iPhone cannibalized the iPad? An asymmetric competition model

Abstract

Product cannibalization is a well‐known phenomenon in marketing, describing the case when a new product steals sales from another product under the same brand. A special case of cannibalization may occur when the older product reacts to the competitive strength of the newer one, absorbing the corresponding market shares. We show that such cannibalization occurred between two Apple products, the iPhone and the iPad, and the first has succeeded at the expense of the second. We propose an innovation diffusion model for asymmetric competition, Lotka‐Volterra with asymmetric competition, allow to test the presence and the extent of the inverse cannibalization phenomenon. A nondimensional representation of the model helps showing the effects of cannibalization on life cycle length.

Forecasting: theory and practice

“…A special application of the LVch model, Lotka-Volterra with asymmetric churn (LVac), is proposed in Guidolin and Guseo (2020). It is based on a statistically oriented reduction: The late entrant behaves as a standard Bass (1969) model that modifies the dynamics and the evolution of the first entrant in a partially overlapped market.…”