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Discontinuous Demand Functions: Estimation and Pricing

Author

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  • Arnoud V. den Boer

    (Korteweg-de Vries Institute for Mathematics and Amsterdam Business School, University of Amsterdam, Amsterdam 1090GE, Netherlands;)

  • N. Bora Keskin

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

Abstract

We consider a dynamic pricing problem with an unknown and discontinuous demand function. There is a seller who dynamically sets the price of a product over a multiperiod time horizon. The expected demand for the product is a piecewise continuous and parametric function of the charged price, allowing for possibly multiple discontinuity points. The seller initially knows neither the locations of the discontinuity points nor the parameters of the demand function but can infer them by observing stochastic demand realizations over time. We measure the seller’s performance by the revenue loss relative to a clairvoyant who knows the underlying demand function with certainty. We construct a dynamic estimation-and-pricing policy that accounts for demand discontinuities, derive the convergence rates of discontinuity- and parameter-estimation errors under this policy, and prove that it achieves near-optimal revenue performance. We also extend our analysis to the cases of time-varying demand discontinuities and inventory constraints.

Suggested Citation

  • Arnoud V. den Boer & N. Bora Keskin, 2020. "Discontinuous Demand Functions: Estimation and Pricing," Management Science, INFORMS, vol. 66(10), pages 4516-4534, October.
    • Handle: RePEc:inm:ormnsc:v:66:y:2020:i:10:p:4516-4534
    DOI: 10.1287/mnsc.2019.3446
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    References listed on IDEAS

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    7. N. Bora Keskin & Yuexing Li & Jing-Sheng Song, 2022. "Data-Driven Dynamic Pricing and Ordering with Perishable Inventory in a Changing Environment," Management Science, INFORMS, vol. 68(3), pages 1938-1958, March.
    8. Kazemi, Mohammad Sadegh & Fotopoulos, Stergios B. & Wang, Xinchang, 2023. "Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution," International Journal of Production Economics, Elsevier, vol. 257(C).
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