Efficient auctions

We exhibit an efficient auction (an auction that maximizes surplus conditional on all available information). For private values, the Vickrey auction (for one good) or its Groves-Clarke extension (for multiple goods) is efficient. We show that the Vickrey and Groves-Clarke auctions can be generalized to attain efficiency when there are common values, if each buyer's information can be represented as a one-dimensional signal. When a buyer's information is multidimensional, no auction is generally efficient. Nevertheless, in a broad class of cases, our auction is constrained-efficient in the sense of being efficient subject to incentive constraints.