Sample Complexity of Posted Pricing for a Single Item

TL;DR

This paper studies the number of samples needed to set near-optimal posted prices for selling a single item to multiple buyers, considering various distribution dependencies and objectives, providing tight bounds on sample complexity.

Contribution

It establishes matching upper and lower bounds on the sample complexity for near-optimal posted pricing across different buyer distribution models and objectives.

Findings

Matching bounds on sample complexity for independent buyer distributions.

Matching bounds on sample complexity for correlated buyer distributions.

Results applicable to both welfare and revenue maximization.

Abstract

Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical and do not work for sequential buyers, posted pricing mechanisms, where fixed prices are set for the item for different buyers, have emerged as a practical and effective alternative. This paper investigates how many samples are needed from buyers' value distributions to find near-optimal posted prices, considering both independent and correlated buyer distributions, and welfare versus revenue maximization. We obtain matching upper and lower bounds (up to logarithmic factors) on the sample complexity for all these settings.