In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. While we show that the allocation problem among valuations with decreasing marginal utilities is NP-hard, we present an efficient greedy 2-approximation algorithm for this case. No such approximation algorithm exists in a setting allowing for complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.
|Original language||American English|
|Number of pages||11|
|State||Published - 2001|
|Event||EC'01: Proceedings of the 3rd ACM Conference on Electronic Commerce - Tampa, FL, United States|
Duration: 14 Oct 2001 → 17 Oct 2001
|Conference||EC'01: Proceedings of the 3rd ACM Conference on Electronic Commerce|
|Period||14/10/01 → 17/10/01|
Bibliographical noteFunding Information:
✩ A preliminary version of this paper has been presented at EC-2001. Supported by grants from the Israeli Ministry of Science and the Israeli Academy of Sciences. Corresponding author. E-mail addresses: firstname.lastname@example.org (D. Lehmann), email@example.com (N. Nisan). § Benny passed away on July 1st, 2004.