Optimal Dsic Auctions for Correlated Private Values : Ex-Post vs. Ex-Interim IR

We study Dominant-Strategy Incentive-Compatible (DSIC) revenue-maximizing auctions (“optimal” auctions) for a single-item and correlated private values. We give tight bounds on the ratio of the revenue of the optimal Ex-Post Individually Rational (EPIR) auction and the revenue of the optimal Ex-Interim Individually Rational (EIIR) auction. This bound is expressed as a non-decreasing function of the expected social welfare of the underlying distribution. In particular, we show a class of distributions on which this ratio cannot be lower bounded by any positive number. Thus, the restriction to EPIR auctions, which has been the de-facto standard in the computer science literature on auctions with correlated values, may significantly reduce the revenue that can be possibly extracted, as the revenue extracted by an EPIR auction might be an arbitrarily small fraction of the revenue extracted by an EIIR auction