Nonlinear anonymous pricing combinatorial auctions
In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant that has won a subset of items knows why his bid was a winning bid and that agents that have not acquired any item easily can detect why they lost. The problem in the combinatorial auction setting is that the winner determination problem is a hard integer programming problem and hence a linear pricing scheme supporting the optimal allocation might not exist. From integer programming duality theory we know that there exist nonlinear anonymous price functions that support the optimal allocation. In this paper we will provide a means to obtain a simple form of a price system that supports the optimal allocation. Our method relies on the fact that we separate the solution of the winner determination problem and the pricing problem. This separation yields a nonlinear price function of a much simpler form compared to when the two problems are solved simultaneously. The pure pricing problem is formulated as a mixedinteger program. The procedure is computationally tested using difficult instances of the combinatorial auctions test suite [16]. The results indicate that the number of extreme prices forming the nonlinear anonymous price system is small.
Year of publication: 
2009


Authors:  Drexl, Andreas ; Jørnsten, Kurt ; Knof, Diether 
Published in: 
European Journal of Operational Research.  Elsevier, ISSN 03772217.  Vol. 199.2009, 1, p. 296302

Publisher: 
Elsevier 
Keywords:  Combinatorial auctions Set packing Strong duality theory Nonlinear anonymous pricing 
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