Chapter 10: Preference Elicitation in Combinatorial Auctions

1 Motivation and introduction The key feature that makes combinatorial auctions (CAs) most appealing is the ability for bidders to express complex preferences over collections of items, involving complementarity and substitutability. It is this generality that makes providing the input to a CA extremely difficult for bidders. In effect, each bidder must provide her valuation function over the space of all bundles of items. More precisely, with m items for sale, there are 2 − 1 bundles over which a bidder may have to provide bids. Requiring all of this information from all bidders is undesirable for several reasons. First, determining one’s valuation for any specific bundle can be computationally demanding (Sandholm, 1993, 2000; Parkes, 1999b; Larson and Sandholm, 2001), thus requiring this computation for exponentially many bundles is impractical. Second, communicating exponentially many bids can be prohibitive (e.g., w.r.t. network traffic). Finally, agents may prefer not to reveal their valuation information for reasons of privacy or long-term competitiveness (Rothkopf et al., 1990). Several approaches have been proposed for addressing the problem. Ascending CAs—see, for example, Parkes (1999a), Wurman and Wellman (2000), Ausubel and Milgrom (2002), Parkes (Chapter 2), and Ausubel and Milgrom (Chapter 3)—provide one means of minimizing the information requirements on bidders by posting prices (sometimes implicitly) on all bundles and ask-