Combinatorial auctions with decreasing marginal utilities

• 成果类型: Article; Proceedings Paper
• 署名作者: Lehmann, Benny; Lehmann, Daniel; Nisan, Noam
• 署名单位: Hebrew University of Jerusalem
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2005.02.006
• 发表日期: 2006
• 页码: 270-296
• 关键词: Combinatorial auctions; decreasing marginal utilities; winner determination

摘要

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. (c) 2005 Elsevier Inc. All rights reserved.