Correlation-Robust Optimal Auctions

Abstract: I study the design of auctions in which the auctioneer is assumed to have information only about the marginal distribution of a generic bidder's valuation, but does not know the correlation structure of the joint distribution of bidders' valuations. I assume that a generic bidder's valuation is bounded and $\bar{v}$ is the maximum valuation of a generic bidder. The performance of a mechanism is evaluated in the worst case over the uncertainty of joint distributions that are consistent with the marginal distribution. For the two-bidder case, the second-price auction with the uniformly distributed random reserve maximizes the worst-case expected revenue across all dominant-strategy mechanisms under certain regularity conditions. For the $N$-bidder ($N\ge3$) case, the second-price auction with the $\bar{v}-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard (a bidder whose bid is not the highest will never be allocated) dominant-strategy mechanisms under certain regularity conditions. When the probability mass condition (part of the regularity conditions) does not hold, the second-price auction with the $s^*-$scaled $Beta (\frac{1}{N-1},1)$ distributed random reserve maximizes the worst-case expected revenue across standard dominant-strategy mechanisms, where $s^*\in (0,\bar{v})$.