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.
For many years the Simultaneous Multi-Round Auction (SMRA) has been the primary auction design for spectrum sales worldwide. Recently, the core-selecting Combinatorial Clock Auction (CCA) has been used as an alternative to the SMRA in a number of countries promising strong incentives for truthful bidding and high efficiency as a result. We analyze the efficiency and auctioneer revenue of the CCA in comparison to SMRA and examine bidding behavior in both formats. The experiments are based on two value models, which resemble single-and multiband spectrum sales in the field. Such applications often allow for thousands of possible bundles. Bidders in the CCA submitted bids for only a fraction of all bundles with a positive valuation. Bundles were selected based on synergies and payoff after the primary bid rounds. As a consequence, we found efficiency of the CCA to be significantly lower than that of SMRA in the multi-band value model and auctioneer revenue of the CCA to be lower in both value models. In addition, we characterize several properties of the auction format, which result from the two-stage design and the payment and activity rules.
We introduce an auction design framework for large markets with hundreds of items and complex bidder preferences. Such markets typically lead to computationally hard allocation problems. Our new framework consists of compact bid languages for sealed-bid auctions and methods to compute second-price rules such as the Vickrey–Clarke–Groves or bidder-optimal, core-selecting payment rules when the optimality of the allocation problem cannot be guaranteed. To demonstrate the efficacy of the approach for a specific, complex market, we introduce a compact bidding language for TV advertising markets and investigate the resulting winner-determination problem and the computation of core payments. For realistic instances of the respective winner-determination problems, very good solutions with a small integrality gap can be found quickly, although closing the integrality gap to find marginally better solutions or prove optimality can take a prohibitively large amount of time. Our subsequent adaptation of a constraint-generation technique for the computation of bidder-optimal core payments to this environment is a practically viable paradigm by which core-selecting auction designs can be applied to large markets with potentially hundreds of items. Such auction designs allow bidders to express their preferences with a low number of parameters, while at the same time providing incentives for truthful bidding. We complement our computational experiments in the context of TV advertising markets with additional results for volume discount auctions in procurement to illustrate the applicability of the approach in different types of large markets. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.2076 . This paper was accepted by Lorin Hitt, information systems.
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