Dynamic selling mechanisms for product differentiation and learning
We consider a firm that designs a vertically differentiated product line for a population of customers 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, formallymeasured 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 theMQS policy is near-optimal.We also prove that, if there exists a certain continuumof informative quality choices, then even a myopic policy thatmakes 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 casewhere the firm simultaneously learns the customers' quality-sensitivity distribution as well as the cost model.
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