Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2005/1: Reflections about pseudo-dual prices in combinatorial auctions

Andreas Drexl () and Kurt Jörnsten ()
Additional contact information
Andreas Drexl: Lehrstuhl für Produktion und Logistik, Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Postal: Lehrstuhl für Produktion und Logistik , Institut für Betriebswirtschaftslehre , Christian-Albrechts-Universität zu Kiel , Olshausenstraße 40 , D-24098 Kiel, Germany
Kurt Jörnsten: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices a set of item prices is called market clearing or equilibrium if all the winning (losing) bids are greater (less) than or equal to the total price of the bundle items. However, the prices for individual items are not readily computed once the winner determination problem is solved. This is due to the duality gap of integer programming caused by the indivisibility of the items. In this paper we reflect on the calculation of approximate or pseudo-dual item prices. In particular, we present a novel scheme based on the aggregation of winning bids. Our analysis is illustrated by means of numerical examples.

Keywords: Combinatorial auctions; set packing; dual prices

JEL-codes: D44

15 pages, May 26, 2005

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