2001/10/14 by Benny Lehmann, Daniel Lehmann, Noam Nisan · 3 citations
Decision Sciences · Business, Management and Accounting · Economics, Econometrics and Finance · #Auction Theory and Applications #Consumer Market Behavior and Pricing #Game Theory and Voting Systems
paper · doi:10.1145/501158.501161
openalex publication_date 2001/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.