Statistical Mechanism Design: Robust Pricing, Estimation, and Inference

TL;DR

This paper introduces empirically optimal mechanisms for robust pricing and revenue estimation under consumer uncertainty, providing finite-sample guarantees and tools for statistical inference on profits.

Contribution

It develops a new class of sample-based mechanisms with strong revenue guarantees and a toolkit for statistical inference, addressing unknown consumer type distributions.

Findings

Mechanisms achieve near-optimal revenue with finite samples.

Provides methods for confidence intervals and hypothesis testing on profits.

Enhances robustness in pricing strategies under consumer uncertainty.

Abstract

This paper tackles challenges in pricing and revenue projections due to consumer uncertainty. We propose a novel data-based approach for firms facing unknown consumer type distributions. Unlike existing methods, we assume firms only observe a finite sample of consumers' types. We introduce \emph{empirically optimal mechanisms}, a simple and intuitive class of sample-based mechanisms with strong finite-sample revenue guarantees. Furthermore, we leverage our results to develop a toolkit for statistical inference on profits. Our approach allows to reliably estimate the profits associated for any particular mechanism, to construct confidence intervals, and to, more generally, conduct valid hypothesis testing.