2021/05/10 by Zhang, Wanchang
#FOS: Economics and business #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2105.04697
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 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≥3) case, the second-price auction with the v-scaled Beta ((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 ((1)/(N-1),1) distributed random reserve maximizes the worst-case expected revenue across standard dominant-strategy mechanisms, where s^*∈ (0,v).