We design and analyze approximately revenue-maximizing auctions in general single-parameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation distributions are a priori unknown to the seller. Despite this handicap, we show how to obtain approximately optimal expected revenue -nearly as large as what could be obtained if the distributions were known in advance -under quite general conditions. Our most general result concerns arbitrary downwardclosed single-parameter environments and valuation distributions that satisfy a standard hazard rate condition. We also assume that no bidder has a unique attribute value, which is obviously necessary with unknown and attributedependent valuation distributions. Here, we give an auction that, for every such environment and unknown valuation distributions, has expected revenue at least a constant fraction of the expected optimal welfare (and hence revenue). A key idea in our auction is to associate each bidder with another that has the same attribute, with the second bidder's valuation acting as a random reserve price for the first. Conceptually, our analysis shows that even a single sample from a distribution -the second bidder's valuation -is sufficient information to obtain near-optimal expected revenue, even in quite general settings.
The most relevant to this work is REF 's single-sampling auction, which showed that with one sample from each bidder's valuation distribution, the VCG auction with the samples as reserve prices gives a 4-approximation to the optimal revenue, when the distributions are regular.
Revenue maximization with a single sample
EC '10
Mathematics Computer Science