Informational limitations of ascending combinatorial auctions

We study the inherent limitations of natural widely-used classes of ascending combinatorial auctions. Specifically, we show that ascending combinatorial auctions that do not use both non-linear prices and personalized prices can not achieve social efficiency with general bidder valuations. This casts doubt on the performance that can be achieved using the simpler auctions suggested, e.g., by Kwasnica et al. (2005),Porter et al. (2003) and Wurman and Wellman (2000) and justifies the added complexity in the auctions suggested by, e.g., Parkes and Ungar (2000) and Ausubel and Milgrom (2002). Our impossibility results are robust in several senses: they allow the analysis of all the information that was aggregated during the auction rather than considering only the final price level; they hold for any price update system or payment determination rule; they do not depend on strategic aspects, on computational limitations or on communication capacities. We also show that the loss of efficiency is severe and that only a diminishing fraction of the social welfare may be captured.