Pricing with Samples

Abstract

This paper studies the value of data for pricing purposes. Although pricing is central across industries, little is known about the minimal amount of data needed to achieve good pricing decisions. The present paper proposes a novel approach to quantify the informational content of data, through the introduction of a new class of robust data-driven policies and the development of factor-revealing dynamic programs. Studying the prototypical case of data coming in the form of samples from the willingness to pay of customers, we show that even a few samples (as few as 10) go a very long way in uncovering “good” prices. For example, quite strikingly, against a general class of distributions (monotone increasing hazard rate distributions), a single observation guarantees 64% of the performance an oracle with full knowledge of the distribution would achieve, two samples suffice to ensure 71%, and 10 samples guarantee 80% of such performance.