Revenue Maximization from Finite Samples

Abstract

In the present paper, we study the following fundamental problem: how should a decision-maker price based on a finite and limited number of samples from the distribution of values of customers. The decision-maker's objective is to select a pricing policy with maximum competitive ratio when the value distribution is only known to belong to some general non-parametric class. We study achievable performance for two central classes, regular and monotone hazard rate (mhr) distributions, through a general framework. To date, only results are available for a single sample and two samples. We improve existing results but also obtain the first results on achievable performance as the number of samples increases. At a higher level, this work also provides insights on the value of samples for pricing purposes. For example, against mhr distributions (resp. regular), two samples suffice to ensure 71% (resp. 61%) of optimal oracle performance, and ten samples guarantee $80%$ (resp. $65%$) of such performance. Our analysis relies on the introduction of a new (simple) class of policies and the derivation of tractable lower bounds on their performance through factor revealing dynamic programs.