## Combinatorial Auctions with Decreasing Marginal Utilities (2001)

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Citations: | 137 - 21 self |

### BibTeX

@MISC{Lehmann01combinatorialauctions,

author = {Benny Lehmann and Daniel Lehmann and Noam Nisan},

title = {Combinatorial Auctions with Decreasing Marginal Utilities},

year = {2001}

}

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### Abstract

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.