Pricing with Samples

67 Pages Posted: 19 Mar 2019 Last revised: 2 Jul 2021

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 25, 2019

Abstract

In the present paper, we study a fundamental data-driven pricing problem: how should a decision-maker (optimally) price based on a finite and limited number of samples from the distribution of values of customers. The decision-maker's objective is to select a general pricing policy with maximum worst-case ratio of revenue compared to an oracle with knowledge of the value distribution, when the latter is only known to belong to some general non-parametric class. We study achievable performance for two central classes: regular and monotone hazard rate (mhr) distributions. We develop a novel unified general approach to quantify the performance of mechanisms. The approach allows to characterize optimal performance for the fundamental case of a single sample through lower and upper bounds on the maximin ratio, with corresponding near-optimal mechanisms and near-worst-case distributions. Furthermore, by extending this class of mechanisms to the cases in which more samples are available, we leverage our general approach to analyze a novel family of policies leading to new results on achievable performance as the number of samples increases. At a higher level, this work also uncovers insights on the value of samples for pricing purposes. For example, against mhr distributions, a single sample guarantees 64% of the performance an oracle with full knowledge of the distribution would achieve, two samples suffice to ensure 71%, and ten samples guarantee 80% of such performance.

Keywords: Pricing, data-driven decision-making, robust pricing, value of information, market research, monotone hazard rate distributions, regular distributions, approximation ratio.

Suggested Citation

Allouah, Amine and Bahamou, Achraf and Besbes, Omar, Pricing with Samples (February 25, 2019). Available at SSRN: https://ssrn.com/abstract=3334650 or http://dx.doi.org/10.2139/ssrn.3334650

Amine Allouah

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1601 S. California Ave.
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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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