Combinatorial auctions are used for the efficient allocation of heterogeneous goods and services. They require appropriate software platforms providing automated winner determination and decision support for bidders. Several promising ascending combinatorial auction formats have been developed throughout the past few years based on primal-dual algorithms and linear programming theory. The Ascending Proxy Auction (Ausubel and Milgrom 2006a) and iBundle (Parkes and Ungar 2000) result in Vickrey payoffs when the coalitional value function satisfies buyer submodularity conditions and bidders bid best-response. These auction formats are based on non-linear and personalized ask prices. In addition, there are a number of designs with linear prices that have performed well in experiments (Bichler et al. 2009, Kwasnica et al. 2005. In this paper, we provide the results of lab experiments testing these different auction formats in the same setting. We analyze aggregate metrics, such as efficiency and auctioneer revenue for small and medium-sized value models. In addition, we provide a detailled analysis not only of aggregate performance metrics, but of individual bidding behavior under alternative combinatorial auction formats.

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.

This paper, selected for the category "Best papers from 1959 to 2008", was first published in WIRTSCHAFTSINFORMATIK 47(2)2005:126-134. Combinatorial auctions are promising auction formats for industrial and public procurement. Potential advantages of using combinatorial auctions include lower overall spend, low transaction costs for multi-item negotiations, fairness and market transparency for suppliers as well as high allocative efficiency. A number of fundamental design considerations are relevant to the application of combinatorial auctions in procurement. In addition, procurement specialists need to consider several domain-specific requirements, such as additional side constraints as well as alternative multidimensional bid types.

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