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Combinatorial Auctions with Decreasing Marginal Utilities | | Benny Lehmann
; Daniel Lehmann
; Noam Nisan
; | | Date: |
15 Feb 2002 | | Subject: | Computer Science and Game Theory ACM-class: J.4 | cs.GT | | Abstract: | In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular 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. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented. | | Source: | arXiv, cs.GT/0202015 | | Services: | Forum | Review | PDF | Favorites | |
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