On the limitations of data-based price discrimination
It addresses a fundamental problem in economics and machine learning for sellers using data-driven pricing, revealing incremental insights into the limitations of price discrimination under uncertainty.
This paper investigates whether third-degree price discrimination (3PD) remains superior to uniform pricing when sellers set prices based on limited samples rather than full distribution knowledge, finding that the revenue comparison becomes ambiguous due to statistical learning challenges like the curse of dimensionality and small sample issues.
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.