Diffusion of two brands in competition: cross-brand effect

TL;DR

This paper analyzes the competitive diffusion of two brands using a Bass-based model, sensitivity analysis, and comparison with an agent-based Potts model, revealing conditions for similar diffusion patterns.

Contribution

It introduces a detailed analysis of cross-brand effects in diffusion models and compares two different modeling approaches for better understanding of brand competition dynamics.

Findings

Models match diffusion curves when cross coefficients are zero.

Sensitivity analysis highlights impact of cross-brand parameters.

Agent-based and differential equation models align under specific conditions.

Abstract

We study the equilibrium points of a system of equations corresponding to a Bass based model that describes the diffusion of two brands in competition. To increase the understanding of the effects of the cross-brand parameters, we perform a sensitivity analysis. Finally, we show a comparison with an agent-based model inspired in the Potts model. Conclusions include that both models give the same diffusion curves only when the cross coeficients are not null.