  We revisit the problem of designing the profit-maximizing single-item
auction, solved by Myerson in his seminal paper for the case in which bidder
valuations are independently distributed. We focus on general joint
distributions, seeking the optimal deterministic incentive compatible auction.
We give a geometric characterization of the optimal auction, resulting in a
duality theorem and an efficient algorithm for finding the optimal
deterministic auction in the two-bidder case and an NP-completeness result for
three or more bidders.
