Optimal Pricing with a Single Point

87 Pages Posted: 11 Mar 2021 Last revised: 28 Mar 2022

See all articles by Amine Allouah

Amine Allouah

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Achraf Bahamou

Columbia University - Department of Industrial Engineering and Operations Research

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations

Date Written: February 26, 2021

Abstract

We study the following fundamental data-driven pricing problem. How can/should a decision-maker price its product based on data at a single historical price? How valuable is such data? We consider a decision-maker who optimizes over (potentially randomized) pricing policies to maximize the worst-case ratio of the revenue she can garner compared to an oracle with full knowledge of the distribution of values, when the latter is only assumed to belong to a broad non-parametric set. In particular, our framework applies to the widely used regular and monotone non-decreasing hazard rate (mhr) classes of distributions. For settings where the seller knows the exact probability of sale associated with one historical price or only a confidence interval for it, we fully characterize optimal performance and near-optimal pricing algorithms that adjust to the information at hand. The framework we develop is general and allows to characterize optimal performance for deterministic or more general randomized mechanisms, and leads to fundamental novel insights on the value of data for pricing. As examples, against mhr distributions, we show that it is possible to guarantee 85% of oracle performance if one knows that half of the customers have bought at the historical price, and if only 1% of the customers bought, it still possible to guarantee 51% of oracle performance.

Keywords: pricing, data-driven algorithms, conversion rate, limited information, randomized algorithms, value of data

Suggested Citation

Allouah, Amine and Bahamou, Achraf and Besbes, Omar, Optimal Pricing with a Single Point (February 26, 2021). Available at SSRN: https://ssrn.com/abstract=3801056 or http://dx.doi.org/10.2139/ssrn.3801056

Amine Allouah

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Achraf Bahamou

Columbia University - Department of Industrial Engineering and Operations Research ( email )

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New York, NY 10027
United States

HOME PAGE: http://www.columbia.edu/~ab4689/

Omar Besbes (Contact Author)

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

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