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A Computational Analysis of Linear Price Iterative Combinatorial Auction Formats

Department of Informatics, Technische Universität München, 85748 Garching, Germany
Department of Informatics, Technische Universität München, 85748 Garching, Germany
Department of Informatics, Technische Universität München, 85748 Garching, Germany
bichler{at}in.tum.de
shabalin{at}in.tum.de
pikovsky{at}mytum.de

Iterative combinatorial auctions (ICAs) are IT-based economic mechanisms where bidders submit bundle bids in a sequence and an auctioneer computes allocations and ask prices in each auction round. The literature in this field provides equilibrium analysis for ICAs with nonlinear personalized prices under strong assumptions on bidders' strategies. Linear pricing has performed very well in the lab and in the field. In this paper, we compare three selected linear price ICA formats based on allocative efficiency and revenue distribution using different bidding strategies and bidder valuations. The goal of this research is to benchmark different ICA formats and design and analyze new auction rules for auctions with pseudodual linear prices. The multi-item and discrete nature of linear price iterative combinatorial auctions and the complex price calculation schemes defy much of the traditional game theoretical analysis in this field. Computational methods can be of great help in exploring potential auction designs and analyzing the virtues of various design options. In our simulations, we found that ICA designs with linear prices performed very well for different valuation models even in cases of high synergies among the valuations. There were, however, significant differences in efficiency and in the revenue distributions of the three ICA formats. Heuristic bidding strategies using only a few of the best bundles also led to high levels of efficiency. We have also identified a number of auction rules for ask price calculation and auction termination that have shown to perform very well in the simulations.

Key Words: iterative combinatorial auction; pseudodual prices; allocative efficiency; computational experiment
History: This paper was received on June 13, 2006.