  We consider a robust version of the revenue maximization problem, where a
single seller wishes to sell $n$ items to a single unit-demand buyer. In this
robust version, the seller knows the buyer's marginal value distribution for
each item separately, but not the joint distribution, and prices the items to
maximize revenue in the worst case over all compatible correlation structures.
We devise a computationally efficient (polynomial in the support size of the
marginals) algorithm that computes the worst-case joint distribution for any
choice of item prices. And yet, in sharp contrast to the additive buyer case
(Carroll, 2017), we show that it is NP-hard to approximate the optimal choice
of prices to within any factor better than $n^{1/2-\epsilon}$. For the special
case of marginal distributions that satisfy the monotone hazard rate property,
we show how to guarantee a constant fraction of the optimal worst-case revenue
using item pricing; this pricing equates revenue across all possible
correlations and can be computed efficiently.
