Posting Prices with Unknown Distributions

Abstract

We consider a dynamic auction model, where bidders sequentially arrive to the market. The values of the bidders for the item for sale are independently drawn from a distribution, but this distribution is unknown to the seller. The seller offers a personalized take-it-or-leave-it price for each arriving bidder and aims to maximize revenue. We study how well can such sequential posted-price mechanisms approximate the optimal revenue that would be achieved if the distribution was known to the seller. On the negative side, we show that sequential posted-price mechanisms cannot guarantee a constant fraction of this revenue when the class of candidate distributions is unrestricted. We show that this impossibility holds even for randomized mechanisms and even if the set of possible distributions is very small or when the seller has a prior distribution over the candidate distributions. On the positive side, we devise a simple posted-price mechanism that guarantees a constant fraction of the known-distribution revenue when all candidate distributions exhibit the monotone hazard rate property.