Discontinuous Demand Functions: Estimation and Pricing

Forthcoming in Management Science

70 Pages Posted: 20 Jul 2017 Last revised: 10 Jul 2019

See all articles by Arnoud den Boer

Arnoud den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics; University of Amsterdam Business School

N. Bora Keskin

Duke University - Fuqua School of Business

Date Written: June 13, 2019

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.

Keywords: Revenue management, pricing, estimation, exploration-exploitation, demand discontinuity.

Suggested Citation

den Boer, Arnoud and Keskin, N. Bora, Discontinuous Demand Functions: Estimation and Pricing (June 13, 2019). Forthcoming in Management Science, Available at SSRN: https://ssrn.com/abstract=3003984 or http://dx.doi.org/10.2139/ssrn.3003984

Arnoud Den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics ( email )

Netherlands

University of Amsterdam Business School ( email )

Roetersstraat 18
Amsterdam, 1018WB
Netherlands

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

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