Welfare and profit maximization with production costs

Avrim Blum, Anupam Gupta, Yishay Mansour, Ankit Sharma

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Combinatorial Auctions are a central problem in Algorithmic Mechanism Design: pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare, revenue, or profit). The problem has been well-studied in the case of limited supply (one copy of each item), and in the case of digital goods (the seller can produce additional copies at no cost). Yet in the case of resources - oil, labor, computing cycles, etc. - neither of these abstractions is just right: additional supplies of these resources can be found, but at increasing difficulty (marginal cost) as resources are depleted. In this work, we initiate the study of the algorithmic mechanism design problem of combinatorial pricing under increasing marginal cost. The goal is to sell these goods to buyers with unknown and arbitrary combinatorial valuation functions to maximize either the social welfare, or the seller's profit, specifically we focus on the setting of posted item prices with buyers arriving online. We give algorithms that achieve constant factor approximations for a class of natural cost functions - linear, low-degree polynomial, logarithmic - and that give logarithmic approximations for more general increasing marginal cost functions (along with a necessary additive loss). We show that these bounds are essentially best possible for these settings.

Original languageEnglish (US)
Title of host publicationProceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
PublisherIEEE Computer Society
Number of pages10
ISBN (Print)9780769545714
StatePublished - 2011
Event2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States
Duration: Oct 22 2011Oct 25 2011

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Other2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Country/TerritoryUnited States
CityPalm Springs, CA

ASJC Scopus subject areas

  • General Computer Science


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