Distributionally Robust Pricing in Independent Private Value Auctions

TL;DR

This paper investigates robust reserve pricing in second-price auctions with private, iid values, showing that setting the reserve to the seller's valuation maximizes worst-case revenue and that this approach is asymptotically optimal as bidders increase.

Contribution

It proves that the optimal worst-case reserve price is the seller's valuation, providing new insights into robust auction design under limited distributional knowledge.

Findings

Optimal reserve is the seller's valuation.

Reserve prices below valuation are also optimal with many bidders.

As bidders grow large, setting reserve to seller's value is asymptotically optimal.

Abstract

A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. Using an indirect technique, we prove that it is always optimal to set the reserve price to the seller's own valuation. However, the maxmin reserve price may not be unique. If the number of bidders is sufficiently high, all prices below the seller's valuation, including zero, are also optimal. A second-price auction with the reserve equal to seller's value (or zero) is an asymptotically optimal mechanism (among all ex post individually rational mechanisms) as the number of bidders grows without bound.