Combinatorial auctions with decreasing marginal utilities

Benny Lehmann; Daniel Lehmann; Noam Nisan

doi:10.1145/501158.501161

Combinatorial auctions with decreasing marginal utilities

Benny Lehmann
, Daniel Lehmann^*
, Noam Nisan

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

161 Scopus citations

Abstract

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	English
Title of host publication	EC'01
Subtitle of host publication	Proceedings of the 3rd ACM Conference on Electronic Commerce
Publisher	Association for Computing Machinery (ACM)
Pages	18-28
Number of pages	11
ISBN (Print)	9781581133875
DOIs	https://doi.org/10.1145/501158.501161
State	Published - 14 Oct 2001
Event	3rd ACM Conference on Electronic Commerce, EC 2001 - Tampa, FL, United States Duration: 14 Oct 2001 → 17 Oct 2001

Publication series

Name	Proceedings of the ACM Conference on Electronic Commerce

Conference

Conference	3rd ACM Conference on Electronic Commerce, EC 2001
Country/Territory	United States
City	Tampa, FL
Period	14/10/01 → 17/10/01

Access to Document

10.1145/501158.501161

Cite this

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title = "Combinatorial auctions with decreasing marginal utilities",

abstract = "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.",

author = "Benny Lehmann and Daniel Lehmann and Noam Nisan",

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doi = "10.1145/501158.501161",

language = "אנגלית",

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note = "3rd ACM Conference on Electronic Commerce, EC 2001 ; Conference date: 14-10-2001 Through 17-10-2001",

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Lehmann, B, Lehmann, D & Nisan, N 2001, Combinatorial auctions with decreasing marginal utilities. in EC'01: Proceedings of the 3rd ACM Conference on Electronic Commerce. Proceedings of the ACM Conference on Electronic Commerce, Association for Computing Machinery (ACM), pp. 18-28, 3rd ACM Conference on Electronic Commerce, EC 2001, Tampa, FL, United States, 14/10/01. https://doi.org/10.1145/501158.501161

Combinatorial auctions with decreasing marginal utilities. / Lehmann, Benny; Lehmann, Daniel ; Nisan, Noam.
EC'01: Proceedings of the 3rd ACM Conference on Electronic Commerce. Association for Computing Machinery (ACM), 2001. p. 18-28 (Proceedings of the ACM Conference on Electronic Commerce).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

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Combinatorial auctions with decreasing marginal utilities

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