Combinatorial Auction Design Aleksandar Peke ˇ c • Michael H. Rothkopf Decision Sciences, The Fuqua School of Business, Duke University, Durham, North Carolina 27708-0120 RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, New Jersey 08854-8003 pekec@duke.edu • rothkopf@rutcor.rutgers.edu C ombinatorial auctions have two features that greatly affect their design: computational complexity of winner determination and opportunities for cooperation among com- petitors. Dealing with these forces trade-offs between desirable auction properties such as allocative efficiency, revenue maximization, low transaction costs, fairness, failure freeness, and scalability. Computational complexity can be dealt with algorithmically by relegating the computational burden to bidders, by maintaining fairness in the face of computational limitations, by limiting biddable combinations, and by limiting the use of combinatorial bids. Combinatorial auction designs include single-round, first-price sealed bidding, Vickrey- Clarke-Groves (VCG) mechanisms, uniform and market-clearing price auctions, and iterative combinatorial auctions. Combinatorial auction designs must deal with exposure problems, threshold problems, ways to keep the bidding moving at a reasonable pace, avoiding and resolving ties, and controlling complexity. ( Auction Design; Combinatorial Bidding; Bidding with Synergies ) 1. Introduction Auctions have recently come into the spotlight because of their use in deregulation and their explo- sive propagation on the Internet. Sales of the rights to the use of radio spectrum by the U.S. Federal Communications Commission (FCC) and daily elec- tricity supply auctions are examples of recent inno- vations in the use of auctions in deregulation. While millions participate in Internet auctions such as those on Ebay.com, the main impact of auctions has been in business-to-business (B2B) applications. For exam- ple, in its remarkable makeover that led to the title “E-Business of the Year 2000” by InternetWeek magazine, General Electric has pushed toward online auctions for most of its procurement operations, con- ducting more than $6 billion in online auctions in 2000 (General Electric Corp. 2001). It is likely that online auctions will continue to play an impor- tant role in procurement and, perhaps, in other aspects of business operations of most successful large organizations. Auctions have a particularly convenient property of aggregating information. Even if no information on the bidders’ valuations of an item is available, if there is sufficient demand, the bidtaker can arrange the sale of an item to the bidder who values it the most at a “fair” price. However, when multiple items are for sale, potential auction mechanisms may be impracti- cal due to inherent complexities. There may be fur- ther complexities in analyzing equilibrium bidding strategies. While some theoretical limits still constrain what can realistically be done in practice, what is practical has changed considerably with advances in both communications and computational technology. Combinatorial auctions—simultaneous multiple-item auctions that allow submission of “all or nothing bids” for combinations of the items being sold—are an important example. Bids on combinations of items are important to bid- ders whose value for combinations is greater than the sum of their values for the individual items in the combination. Such “complementarities” com- monly arise from cost savings in procurement (such as back hauls in trucking) and synergies between assets (such as spectrum licenses for adjacent areas). Complementarities appear to be the main practical 0025-1909/03/4911/1485 1526-5501 electronic ISSN Management Science © 2003 INFORMS Vol. 49, No. 11, November 2003, pp. 1485–1503