Dynamic Selling Mechanisms for Product Differentiation and Learning
Forthcoming in Operations Research
64 Pages Posted: 25 Nov 2014 Last revised: 7 Oct 2018
Date Written: May 20, 2018
We consider a firm that designs a vertically differentiated product line for a population of cus- tomers with heterogeneous quality sensitivities. The firm faces an uncertainty about the cost of quality, 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. Based on this, we design a minimum quality standard (MQS) policy that mimics the salient features of the optimal product differentiation policy and prove 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. Finally, we extend our results to the case where the firm simultaneously learns the customers’ quality sensitivity distribution as well as the cost model.
Keywords: Dynamic programming, self-selection, Bayesian learning, exploration-exploitation
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