Statistical Mechanism Design: Robust Pricing, Estimation, and Inference (2405.17178v1)

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.