Dynamic Selling Mechanisms for Product Differentiation and Learning

Abstract

We consider a firm that designs a menu of vertically differentiated products for a population of customers with heterogeneous quality sensitivities. The firm faces an uncertainty about production costs, and we formulate this uncertainty as a belief distribution on a set of cost models. Over a time horizon of T periods, the firm can dynamically adjust its menu and make noisy observations on the underlying cost model through customers’ purchasing decisions. We characterize how optimal product differentiation depends on the “informativeness” of quality choices, formally measured by a contrast-to-noise ratio defined on the firm’s feasible quality set. We prove that, if there exist informative quality choices, then the optimal product differentiation policy improves the product quality to accelerate information accumulation and exercises the most extreme experimentation on less quality-sensitive customers. We design a minimum quality standard (MQS) policy that mimics the aforementioned features of the optimal policy and show that the MQS policy is near-optimal. We also prove that, if there exists a certain continuum of informative quality choices, then even a myopic policy that makes no attempt to learn exhibits near-optimal profit performance. This stands in stark contrast to the poor performance of myopic policies in pricing and learning problems in the absence of product differentiation.