  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 $s^*\in
(0,\bar{v})$.
