Dynamic Pricing for Vertically Differentiated Products

This paper studies the seller’s optimal pricing policies for a family of substitute perishable products. The seller aims to maximize her expected cumulative revenues over a finite selling horizon. At each demand epoch, the arriving customer observes the set of substitute products with positive inventory together with their prices. Based on this information as well as the customer’s own budget constraint, he either buys one of the available products, or leaves the system without making any purchase. We propose a choice model where a fixed ranking of the products is decided by the quality-price combination. We show the monotonicity property of the optimal prices with respect to quality, inventory and time-to-go. We derive the distribution-free pricing methodology and obtain the robust bounds on the price increment through the first-order Taylor approximation. Our work also sheds light on the assortment design in terms of choosing the breadth of the product quality range as well as the number of products in the assortment.