Optimal Item Pricing in Online Combinatorial Auctions

José Correa, Andrés Cristi*, Andrés Fielbaum, Tristan Pollner, S. Matthew Weinberg

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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We consider a fundamental pricing problem in combinatorial auctions. We are given a set of indivisible items and a set of buyers with randomly drawn monotone valuations over subsets of items. A decision maker sets item prices and then the buyers make sequential purchasing decisions, taking their favorite set among the remaining items. We parametrize an instance by d, the size of the largest set a buyer may want. Our main result asserts that there exist prices such that the expected (over the random valuations) welfare of the allocation they induce is at least a factor 1/ (d+ 1 ) times the expected optimal welfare in hindsight. Moreover we prove that this bound is tight. Thus, our result not only improves upon the 1/ (4 d- 2 ) bound of Dütting et al., but also settles the approximation that can be achieved by using item prices. We further show how to compute our prices in polynomial time. We provide additional results for the special case when buyers’ valuations are known (but a posted-price mechanism is still desired).

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization
Subtitle of host publicationProceedings of the 23rd International Conference, IPCO 2022
EditorsKaren Aardal, Laura Sanità
ISBN (Electronic)978-3-031-06901-7
ISBN (Print)978-3-031-06900-0
Publication statusPublished - 2022
Event23rd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2022 - Eindhoven, Netherlands
Duration: 27 Jun 202229 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13265 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Combinatorial Auctions
  • Online allocations


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