Pricing with Samples
67 Pages Posted: 19 Mar 2019 Last revised: 2 Jul 2021
Date Written: February 25, 2019
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.
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