Optimal deterministic auctions with correlated priors

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, either discrete or Lipschitz-continuous, 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.