A Mathematical Study of Competition and Adoption of Two Consumer Products

This research project aims to construct a competition model between two consumer products in the market based on the Bass Diffusion Model. We want to predict the long-term performance of these two products in the market–whether they will both survive, or only one of them can survive while the other one will be wiped out. This prediction of consumer behaviors can greatly help the management of the firms selling these products. In order to do that, we would like to adopt and modify two well-known models: the Bass Diffusion Model and the Lotka-Volterra Competition Model.  However, one limitation in the Bass Model is that it measures the future performance on only one product, but it is desirable to know how multiple products will interact in the market. For the sake of this research project, we want to focus on the competition between two products. Thus, in our model we would also like to take consideration of the Lotka-Volterra Competition Model, which is a famous ecology model describing the population dynamics of two competing species with scarce resources. The outcome of competition depends on the strength of competition of each species and possibly the initial conditions. With these two models in mind we propose our modified model to predict the long-term behaviors of two consumer products.

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