Optimal and competitive assortments with endogenous pricing under hierarchical consumer choice models’,

T his paper studies assortment planning and pricing for a product category with heterogeneous product types from two brands. We model consumer choice using the nested multinomial logit framework with two different hierarchical structures: a brand-primary model in which consumers choose a brand first, then a product type in the chosen brand, and a type-primary model in which consumers choose a product type first, then a brand within that product type. We consider a centralized regime that finds the optimal solution for the whole category and a decentralized regime that finds a competitive equilibrium between two brands. We find that optimal and competitive assortments and prices have quite distinctive properties across different models. Specifically, with the brand-primary model, both the optimal and the competitive assortments for each brand consist of the most popular product types from the brand. With the type-primary choice model, the optimal and the competitive assortments for each brand may not always consist of the most popular product types of the brand. Instead, the overall assortment in the category consists of a set of most popular product types. The price of a product under the centralized regime can be characterized by a sum of a markup that is constant across all products and brands, its procurement cost, and its marginal operational cost, implying a lower price for more popular products. The markup may be different for each brand and product type under the decentralized regime, implying a higher price for brands with a larger market share. These properties of the assortments and prices can be used as effective guidelines for managers to identify and price the best assortments and to rule out nonoptimal assortments. Our results suggest that to offer the right set of products and prices, category and/or brand managers should create an assortment planning process that is aligned with the hierarchical choice process consumers commonly follow to make purchasing decisions

Product Line Pricing in a Supply Chain

A vertically integrated channel would prefer to coordinate the pricing of its products. In this paper, we investigate drivers of product line pricing decisions in a bilateral monopoly where a manufacturer produces and sells two substitutable or complementary products to a retailer. In a two-stage game, each firm commits credibly in the first stage to a pricing scheme within its own organization: product line pricing (PLP) or nonproduct line pricing (NPLP). In the second stage, depending on the relative balance of power in the supply chain, the firms engage in either a Nash or a leader-follower pricing game. We study the equilibrium of the two-stage game under a general symmetric demand function. With strategic interaction between firms, a firm may choose NPLP as the equilibrium pricing strategy. In particular, when the second stage is a leader-follower game, the price leader chooses PLP, and the follower may choose NPLP only if the inefficiency of using NPLP empowers the follower by increasing the demand sensitivity to the leader's margin. When the second stage is a vertical Nash game, whether NPLP occurs in equilibrium depends on the nature of coupling between demand interdependence and vertical strategic dependence: NPLP can be an equilibrium only if products are demand substitutes (complements) and vertical strategic dependencies are complementary (substitutable). We find that prisoner's dilemma exists in the first stage for both types of second-stage pricing games. In those cases, one firm may have the incentive to commit to a pricing scheme in the first stage prior to its channel partner and steer the supply chain away from prisoner's dilemma.marketing, product line pricing, substitute, complement, equilibrium, vertical strategic interaction