Multidimensional dynamic pricing forwelfare maximization

Aaron Roth, Aleksandrs Slivkins, Jonathan Ullman, Zhiwei Steven Wu

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

9 Scopus citations


We study the problem of a seller dynamically pricing d distinct types of indivisible goods, when faced with the online arrival of unit-demand buyers drawn independently from an unknown distribution. .e goods are not in limited supply, but can only be produced at a limited rate and are costly to produce. .e seller observes only the bundle of goods purchased at each day, but nothing else about the buyer's valuation function. Our main result is a dynamic pricing algorithm for optimizing welfare (including the seller's cost of production) that runs in time and a number of rounds that are polynomial in d and the approximation parameter. We are able to do this despite the fact that (i) the price-response function is not continuous, and even its fractional relaxation is a non-concave function of the prices, and (ii) the welfare is not observable to the seller. We derive this result as an application of a general technique for optimizing welfare over divisible goods, which is of independent interest. When buyers have strongly concave, Holder continuous valuation functions over d divisible goods, we give a general polynomial time dynamic pricing technique. We are able to apply this technique to the of unit demand buyers despite the fact that in that the goods are not divisible, and the natural fractional relaxation of a unit demand valuation is not strongly concave. In order to apply our general technique, we introduce a novel price randomization procedure which has the e.ect of implicitly inducing buyers to "regularize" their valuations with a strongly concave function. Finally, we also extend our results to a limited-supply in which the number of copies of each good cannot be replenished.

Original languageEnglish (US)
Title of host publicationEC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Number of pages18
ISBN (Electronic)9781450345279
StatePublished - Jun 20 2017
Event18th ACM Conference on Economics and Computation, EC 2017 - Cambridge, United States
Duration: Jun 26 2017Jun 30 2017

Publication series

NameEC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation


Other18th ACM Conference on Economics and Computation, EC 2017
Country/TerritoryUnited States

Bibliographical note

Funding Information:
This work was partially supported by NSF grant CNS-1253345, a Sloan Foundation Fellowship, and a DARPA grant. A full version of the paper can be found on arXiv:

Publisher Copyright:
© 2017 ACM.


  • Dynamic pricing
  • Learning
  • Revealed preferences
  • Welfare maximization


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