The design of multidimensional auctions

Procurement auctions usually require the bid to specify several characteristics of the contract to be fulfilled. In this article I study the design of such mechanisms, allowing for a special case of correlation on the firm's costs. I describe the properties of optimal mechanisms and study the design of multidimensional auctions. Contrary to the independent-costs model, to implement the optimal outcome the procurer will need to use a two-stage auction: in the first stage the procurer selects one firm; in the second stage he bargains to readjust the level of quality to be provided.