The Quadratic Core-Selecting Payment Rule for Combinatorial Auctions

Peter Cramton, University of Maryland
Robert Day, University of Connecticut

Abstract

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe, and proposed for use in the FAA’s landing-slot auctions in the United States. Specifically, we compute a unique point “in the core” that minimizes the sum of squared deviations from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a series of economically meaningful and equitable penalties, adding to the perceived “fairness” of this payment rule. Further, we discuss the many benefits of this combinatorial auction paradigm.