Efficient Auctions.

The authors exhibit an efficient auction (i.e., an auction that maximizes expected surplus conditional on all private and public information). In the case of private value, it is well-known that the Vickrey auction (for one good) or its Groves-Clark extension (for multiple goods) is efficient in this sense. However, the Vickrey auction is not efficient once a buyer's valuation can depend on other buyers' private information (the case of "common" or interdependent values). Nevertheless, we show that the Vickrey auctin can be generalized to attain efficiency when there are common values, provided each buyer's information can be represented as a one-dimensional signal (proposition 1 and 2).