On the Prevalence of Small Reserve Prices in Standard Auctions

Abstract

We justify the prevalence of small reserve prices in real-life auctions in spite of empirical findings that suggest optimal reserve prices in those contexts should be higher. We reconcile such discrepancy within the standard paradigm of independent private valuations rather than exploring richer environments capable to rationalize the adoption of small reserve prices. The key driver of our characterization is the uncertainty on the distribution of valuations the seller faces. The uncertainty may arise when the bid sample lacks some variables to determine the valuation distribution or when its point estimate differs from the true distribution. We show that (i) the optimal reserve price under uncertainty decreases as the number of bidders grows; (ii) revenue gains from the optimal reserve price relative to any smaller reserve price disappear at an exponential rate. Finally, we show that when the seller is risk-averse or the amount of uncertainty in the distribution increases, the reserve price decreases further.

Keywords: empirical auction design, optimal reserve price, independent private values, decision under uncertainty

JEL Classification: C57, D44, D81