Computing core payments in combinatorial auctions

Abstract

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 business-to-business commerce. Among the many applications of combinatorial auction research are auctions for shipping-lanes and other procurement in the private sector, as well as auctions for spectrum licenses by the FCC and the proposed auctioning of 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. Much of the literature on combinatorial auctions has focused on the underlying problem of finding an efficient allocation (called the winner-determination problem) which is usually NP-hard, and the problem that the amount of information necessary to describe a bidder’s preferences for all bundles grows exponentially in the number of items. Proposed solutions to these problems include the description of classes of winner-determination instances which are tractable, and the development of “bidding languages” which can express preferences more efficiently, respectively. The problem of strategic difficulty for bidders is often ignored or down-played, however. In order to assume away the bidders’ problem of determining an opti-