Prices and Compact Bidding Languages for Combinatorial Auctions

Combinatorial auctions are currently used for a wide variety of B2B commerce, most notably for industrial procurement of raw materials and shipping lanes, and in the government sector for the allocation of spectrum licenses, wholesale electricity generation, and the proposed control of airport congestion through the auctioning of landing-slot rights. In this paper we summarize the contributions to the study of combinatorial auctions made by Day (2004). We begin by showing an improved technique for the computation of “bidder-Paretooptimal” prices within the “core.” This technique calls for the automated solution of several “winnerdetermination” problems, and like similar combinatorial auction techniques requires each bidder to submit valuations for all bundles of interest to a proxy. Unfortunately, communicating preferences to a proxy may require an exponential amount of information relative to the number of items being auctioned. To address this exponential communication problem, we introduce two new compact bidding languages, and discuss the details, implementations, and relative merits of these approaches.