Product Assortment and Price Competition Under Multinomial Logit Demand

Abstract

The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this paper, we study equilibrium behavior of competing retailers in two settings: i.) when prices are exogenously fixed, and retailers compete in assortments only; and ii.) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that pareto-dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, i.e., assortments might overlap, we show that display constraints drive equilibrium existence properties.

Keywords: assortment planning, competition, choice models, multinomial Logit, pricing