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 cannot achieve social efficiency with general bidder valuations. We also show that the loss of efficiency can be severe and that only a diminishing fraction of the social welfare may be captured. This justifies the added complexity in the auctions suggested by, e.g., Parkes and Ungar (2000)  and Ausubel and Milgrom (2002) .
Bibliographical noteFunding Information:
✩ Authors were supported by grants from the Israeli Academy of Sciences and the USA–Israel Binational Science Foundation. The authors thank Moshe Babaioff, Ron Lavi, Daniel Lehmann, David Parkes and Ilya Segal for helpful discussions. * Corresponding author. Fax: +972 2 5883244. E-mail addresses: email@example.com (L. Blumrosen), firstname.lastname@example.org (N. Nisan).
- Ascending auctions
- Combinatorial auctions
- Non-linear prices
- Package auctions
- Personalized prices