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An analysis of a combinatorial auction

Bjørndal, Mette; Jörnsten, Kurt
Working paper
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URI
http://hdl.handle.net/11250/163613
Date
2001
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  • Discussion papers (FOR) [509]
Abstract
Our objective is to find prices on individual items in a combinatorial auction that support the optimal allocation of bundles of items, i.e. the solution to the winner determination problem of the combinatorial auction. The item-prices should price the winning bundles according to the corresponding winning bids, whereas the bundles that do not belong to the winning set should have strictly positive reduced cost. I.e. the bid on a non-winning bundle is strictly less than the sum of prices of the individual items that belong to the bundle, thus providing information to the bidders why they are not in the winning set. Since the winner determination problem is an integer program, in general we cannot find a linear price-structure with these characteristics. However, in this article we make use of sensitivity analysis and duality in linear programming to obtain this kind of price-information. The ideas are illustrated by means of numerical examples.
Publisher
Norwegian School of Economics and Business Administration. Department of Finance and Management Science
Series
Discussion paper
2001:11

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