On the Power and Limits of Dynamic Pricing in Combinatorial Markets

Ben Berger, Alon Eden*, Michal Feldman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


We study the power and limits of optimal dynamic pricing in combinatorial markets; i.e., dynamic pricing that leads to optimal social welfare. Previous work by Cohen-Addad et al. [EC’16] demonstrated the existence of optimal dynamic prices for unit-demand buyers, and showed a market with coverage valuations that admits no such prices. However, finding the most general class of markets (i.e., valuation functions) that admit optimal dynamic prices remains an open problem. In this work we establish positive and negative results that narrow the existing gap. On the positive side, we provide tools for handling markets beyond unit-demand valuations. In particular, we characterize all optimal allocations in multi-demand markets. This characterization allows us to partition the items into equivalence classes according to the role they play in achieving optimality. Using these tools, we provide a poly-time optimal dynamic pricing algorithm for up to 3 multi-demand buyers. On the negative side, we establish a maximal domain theorem, showing that for every non-gross substitutes valuation, there exist unit-demand valuations such that adding them yields a market that does not admit an optimal dynamic pricing. This result is the dynamic pricing equivalent of the seminal maximal domain theorem by Gul and Stacchetti [JET’99] for Walrasian equilibrium. Yang [JET’17] discovered an error in their original proof, and established a different, incomparable version of their maximal domain theorem. En route to our maximal domain theorem for optimal dynamic pricing, we provide the first complete proof of the original theorem by Gul and Stacchetti.

Original languageEnglish
Title of host publicationWeb and Internet Economics - 16th International Conference, WINE 2020, Proceedings
EditorsXujin Chen, Nikolai Gravin, Martin Hoefer, Ruta Mehta
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9783030649456
StatePublished - 2020
Event16th International Conference on Web and Internet Economics, WINE 2020 - Beijing, China
Duration: 7 Dec 202011 Dec 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12495 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Conference on Web and Internet Economics, WINE 2020


FundersFunder number
European Union?s Horizon 2020 research and innovation program
National Science FoundationCCF-1718549, 1718549, 337122
Horizon 2020 Framework Programme866132
European Research Council
Israel Science Foundation317/17


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