Simple mechanisms for agents with complements

Michal Feldman, Ophir Friedler, Jamie Morgenstern, Guy Reiner

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


We study the efficiency of simple auctions in the presence of complements. Devanur et al. [2015] introduced the single-bid auction, and showed that it has a price of anarchy (PoA) of O(log m) for complement-free (i.e., subadditive) valuations. Prior to our work, no non-trivial upper bound on the PoA of single bid auctions was known for valuations exhibiting complements. We introduce a hierarchy over valuations, where levels of the hierarchy correspond to the degree of complementarity, and the PoA of the single bid auction degrades gracefully with the level of the hierarchy. This hierarchy is a refinement of the Maximum over Positive Hypergraphs (MPH) hierarchy [Feige et al. 2015], where the degree of complementarity d is captured by the maximum number of neighbors of a node in the positive hypergraph representation. We show that the price of anarchy of the single bid auction for valuations of level d of the hierarchy is O(d2 log(m/d)), where m is the number of items. We also establish an improved upper bound of O(dlogm) for a subclass where every hyperedge in the positive hypergraph representation is of size at most 2 (but the degree is still d). Finally, we show that randomizing between the single bid auction and the grand bundle auction has a price of anarchy of at most O(√m) for general valuations. All of our results are derived via the smoothness framework, thus extend to coarse-correlated equilibria and to Bayes Nash equilibria.

Original languageEnglish
Title of host publicationEC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Number of pages17
ISBN (Electronic)9781450339360
StatePublished - 21 Jul 2016
Event17th ACM Conference on Economics and Computation, EC 2016 - Maastricht, Netherlands
Duration: 24 Jul 201628 Jul 2016

Publication series

NameEC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation


Conference17th ACM Conference on Economics and Computation, EC 2016


  • Auctions
  • Price of anarchy
  • Restricted complements


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