Expressing Preferences with Price-Vector Agents in Combinatorial Auctions: A Brief Summary

A combinatorial auction is one in which preferences are expressed for combinations or bundles of items, rather than just for individual items. The importance of combinatorial auctions has grown tremendously in the past 15 years, which have seen an explosion in the use of auction mechanisms in both government allocation problems and businessto-business commerce. Chapter 2 of the dissertation outlines the many applications of combinatorial auction research (as do Anandalingam et al., 2005), including shipping-lane and procurement auctions in the private sector, as well as auctions for spectrum licenses by the FCC and airport landing slots by the FAA in the public sector. In each of these environments, the expression of aggregate information allows the bidders to realize synergies (e.g., economies-of-scale or owning complementary items) while the auction mechanism stimulates competition, aiding the seller of items with more competitive prices. There are, however, two major computational difficulties limiting the implementation of the combinatorial auction paradigm: (1) the underlying problem of finding an efficient allocation (called the winner-determination problem) is NP-hard, and (2) the amount of information necessary to describe a bidder’s preferences for all bundles grows exponentially in the number of items. For each of the real-world environments for which combinatorial auctions have been used (or are being heavily considered for use, as in the airport landing-slot case) the number of items being auctioned is large enough for problem (2) to have a limiting effect. The exponential growth of bundles makes it difficult for bidders to express preferences for every bundle that may be of interest. Clearly, a “bidding language” is necessary to ease the burden of preference expression, helping bidders by placing bids on many bundles simultaneously. The development of an easier to use language of preference expression can increase the efficiency of the auction, both by achieving better outcomes, and by reducing the time spent by the bidders communicating their preferences. The development of a bidding language to aid the bidder with problem (2) should be coupled with the development of a practically implementable solution technique, simultaneously addressing the auctioneer’s difficulty, (1) above. Viable solutions to this problem involve both restricted versions of the NP-hard winner-determination problem that remain NP-hard but are smaller in scale, and restricted versions that are polynomially solvable, but then are more