On the limitations of data-based price discrimination

TL;DR

This paper investigates the limitations of data-driven third degree price discrimination, revealing that sample-based pricing strategies can be ambiguous in revenue performance compared to uniform pricing due to statistical learning challenges.

Contribution

It demonstrates that sample-based price discrimination may not always outperform uniform pricing, highlighting fundamental limitations in data-driven pricing strategies.

Findings

Sample-based 3PD can underperform compared to uniform pricing.

Revenue comparison between 3PD and uniform pricing is ambiguous.

Statistical learning challenges affect data-driven pricing effectiveness.

Abstract

The classic third degree price discrimination (3PD) model requires the knowledge of the distribution of buyer valuations and the covariate to set the price conditioned on the covariate. In terms of generating revenue, the classic result shows that 3PD is at least as good as uniform pricing. What if the seller has to set a price based only on a sample of observations from the underlying distribution? Is it still obvious that the seller should engage in 3PD? This paper sheds light on these fundamental questions. In particular, the comparison of the revenue performance between 3PD and uniform pricing is ambiguous overall when prices are set based on samples. This finding is in the nature of statistical learning under uncertainty: a curse of dimensionality, but also other small sample complications.