Welfare and revenue guarantees for competitive bundling equilibrium

Shahar Dobzinski, Michal Feldman, Inbal Talgam-Cohen, Omri Weinstein*

*Corresponding author for this work

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

6 Scopus citations


Competitive equilibrium, the central equilibrium notion in markets with indivisible goods, is based on pricing each good such that the demand for goods equals their supply and the market clears. This equilibrium notion is not guaranteed to exist beyond the narrow case of substitute goods, might result in zero revenue even when consumers value the goods highly, and overlooks the widespread practice of pricing bundles rather than individual goods. Alternative equilibrium notions proposed to address these shortcomings have either made a strong assumption on the ability to withhold supply in equilibrium, or have allowed an exponential number of prices. In this paper we study the notion of competitive bundling equilibrium – a competitive equilibrium over the market induced by partitioning the goods into bundles. Such an equilibrium is guaranteed to exist, is succinct, and satisfies the fundamental economic condition of market clearance. We establish positive welfare and revenue guarantees for this solution concept: For welfarewe show that inmarkets with homogeneous goods, there always exists a competitive bundling equilibrium that achieves a logarithmic fraction of the optimal welfare. We also extend this result to establish nontrivial welfare guarantees for markets with heterogeneous goods. For revenue we show that in a natural class of markets for which competitive equilibrium does not guarantee positive revenue, there always exists a competitive bundling equilibrium that extracts as revenue a logarithmic fraction of the optimal welfare. Both results are tight.

Original languageAmerican English
Title of host publicationWeb and Internet Economics - 11th International Conference, WINE 2015, Proceedings
EditorsGuido Schäfer, Evangelos Markakis
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783662489949
StatePublished - 2015
Externally publishedYes
Event11th International Conference on Web and Internet Economics, WINE 2015 - Amsterdam, Netherlands
Duration: 9 Dec 201512 Dec 2015

Publication series

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


Conference11th International Conference on Web and Internet Economics, WINE 2015

Bibliographical note

Funding Information:
M. Feldman—partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement number 337122.

Funding Information:
S. Dobzinski—Incumbent of the Lilian and George Lyttle Career Development Chair. Supported in part by the I-CORE program of the planning and budgeting committee and the Israel Science Foundation 4/11 and by EU CIG grant 618128.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.


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