10 - Quadratic Core-Selecting Payment Rules for Combinatorial Auctions

Summary

Introduction

Combinatorial auctions represent one of the most prominent areas of research in the intersection of Operations Research (OR) and Economics. First proposed for practical governmental applications by Rassenti et al. (1982), a combinatorial auction (CA) is an auction for many items in which bidders submit bids on combinations of items, or packages. CAs also are referred to as “package auctions” or auctions with “package bidding.” In a general CA, a bidder may submit bids on any arbitrary collection of packages. The “winner-determination problem” identifies the value maximizing assignment given the package bids. This problem is as complex as the Weighted Set-Packing problem, and hence NP-hard (see Rothkopf et al. 1998).

Thus, in the many real-world applications of CAs, the computational techniques of OR facilitate more efficient economic outcomes in environments too complex for classical (i.e., non-computational) economic theory. Conversely, the game-theoretic framework surrounding CAs provides a host of new computational challenges and optimization problems for OR.

One critical element of any CA is the pricing rule, which determines what each winner pays for the package won. In this paper, we present a new class of optimization based pricing rules for combinatorial auctions in general, demonstrate some of their unique features, and elaborate upon some properties of the larger class of core-selecting mechanisms. We also describe the use of this algorithm for recent and upcoming spectrum-license auctions in the United Kingdom, for upcoming spectrum auctions in several European countries (e.g., the Netherlands, Denmark, Portugal, and Austria), and for use in the United States for the Federal Aviation Administration's (FAA) proposed allocation of landing rights to control congestion at airports. Further, we provide the relevant economic interpretation and theoretical basis for our algorithm's various features.

The use of auctions for allocating spectrum-license-rights to telecommunications companies gained prominence in 1994 when the Federal Communications Commission (FCC) began to use a Simultaneous Ascending Auction (SAA) to sell spectrum licenses in the United States. The initial design, which is still used today with only slight modifications, avoided the idea of a “combinatorial” or “package” auction, in which bidders bid on packages of licenses because of the inherent computational difficulty.