Optimal Pricing Under Diffusion-Choice Models

Abstract

We develop a solution approach to the centralized pricing problem of a firm managing multiple substitutable products. Demand of these products undergoes a diffusion process, and customers choose among the products, with the choice probability of each product given by the logit model. We examine the firm’s optimal pricing problem when product demand can be described by such “diffusion-choice” models. In particular, we focus on two models with proven merits and study a generalized version of the two models. To our knowledge, our work is the first to study the multiproduct pricing problem under the integrated diffusion-choice models, which are of both theoretical appeal and practical advantage. We establish uniqueness of the optimal solution and propose an efficient solution approach in addition to characterizing the optimal prices and their time trend. We show that the price trend can be attributed to diffusion dynamics as well as intertemporal changes in product costs and customer price sensitivity, all of which are integrated into a unified framework in this paper. Our model applies to both simultaneous and sequential product introductions and adapts to stochastic demand.