Combinatorial Scoring Auctions

This paper is concerned with a combinatorial, multi-attribute procurement mechanism called combinatorial scoring auction. In the setting that we analyze, private information of the suppliers is multi-dimensional. The buyer wants to procure several items at once. Subsets of these items are characterized by a price as well as by a number of non-monetary attributes called quality (e.g. completion time). The suppliers submit offers specifying prices and quality levels for these subsets. These offers are evaluated according to a quasi-linear scoring rule. Based on the resulting scores suppliers win contracts for the delivery of certain items. Such a contract only specifies the set of items a supplier has to deliver and a score that he has to meet. The decision about the specific price-quality combination yielding this contracted score is at the discretion of the supplier who aims at optimizing his own profit. We analyze the equilibria in such auctions and show the link between combinatorial scoring auctions and combinatorial price-only auctions. We demonstrate how this link can be used to employ preexisting knowledge about the equilibrium behavior in regular price-only auctions in the strategic analysis of combinatorial scoring auctions. Our results are the multi-item extension to the results of Asker and Cantillon (2007)