Combinatorial auctions with decreasing marginal utilities |
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Authors: | Benny Lehmann Daniel Lehmann Noam Nisan |
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Affiliation: | School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel |
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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. |
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Keywords: | Combinatorial auctions Decreasing marginal utilities Winner determination |
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