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Dynamic Selling Mechanisms for Product Differentiation and Learning


  • N. Bora Keskin

    () (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • John R. Birge

    () (Booth School of Business, University of Chicago, Chicago, Illinois 60637)


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, 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.

Suggested Citation

  • N. Bora Keskin & John R. Birge, 2019. "Dynamic Selling Mechanisms for Product Differentiation and Learning," Operations Research, INFORMS, vol. 67(4), pages 1069-1089, July.
  • Handle: RePEc:inm:oropre:v:67:y:2019:i:4:p:1069-1089
    DOI: 10.1287/opre.2018.1805

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    1. Michael Jong Kim, 2020. "Variance Regularization in Sequential Bayesian Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 966-992, August.

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