Optimal Pricing with a Single Point

75 Pages Posted: 11 Mar 2021

See all articles by Amine Allouah

Amine Allouah

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Achraf Bahamou

affiliation not provided to SSRN

Omar Besbes

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 observations at a single historical price? The decision-maker optimizes over (potentially randomized) pricing policies to maximize the worst-case ratio of the revenue it can garner compared to an oracle with full knowledge of the distribution of values, when the latter is only assumed to belong to 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. 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. The framework we develop leads to new insights on the value of information for pricing, as well as the value of randomization. In addition, it is general and allows to characterize optimal deterministic mechanisms and incorporate uncertainty in the probability of sale.

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

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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1601 S. California Ave.
Palo Alto, CA 94304
United States

Achraf Bahamou

affiliation not provided to SSRN

Omar Besbes (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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