Algorithmic pricing via virtual valuations

Shuchi Chawla*, Jason D. Hartline, Robert Kleinberg

*Corresponding author for this work

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

163 Scopus citations


Algorithmic pricing is the computational problem that sellers (e.g.,in supermarkets) face when trying to set prices for their items to maximize their profit in the presence of a known demand. Guruswami etal. (SODA, 2005) proposed this problem and gave logarithmic approximations (in the number of consumers) for the unit-demand and single-parameter cases where there is a specific set of consumers and their valuations for bundles are known precisely. Subsequently several versions of the problem have been shown to have poly-logarithmic in approximability. This problem has direct ties to the important open question of better understanding the Bayesian optimal mechanism in multi-parameter agent settings; however, for this purpose approximation factors logarithmic in the number of agents are inadequate. It is therefore of vital interest to consider special cases where constant approximations are possible. We consider the unit-demand variant of this pricing problem. Here a consumer has a valuation for each different item and their value for aset of items is simply the maximum value they have for any item in the set. Instead of considering a set of consumers with precisely known preferences, like the prior algorithmic pricing literature, we assume that the preferences of the consumers are drawn from a distribution. This is the standard assumption in economics; furthermore, the setting of a specific set of customers with specific preferences, which is employed in all of the prior work in algorithmic pricing, is a special case of this general Bayesian pricing problem, where there is a discrete Bayesian distribution for preferences specified by picking one consumer uniformly from the given set of consumers. Notice that the distribution over the valuations for the individual items that this generates is obviously correlated. Our work complements these existing works by considering the case where the consumer's valuations for the different items are independent random variables. Our main result is a constant approximation algorithm for this problem that makes use of an interesting connection between this problem and the concept of virtual valuations from the single-parameter Bayesian optimal mechanism design literature.

Original languageEnglish (US)
Title of host publicationEC'07 - Proceedings of the Eighth Annual Conference on Electronic Commerce
Number of pages9
StatePublished - 2007
Event8th ACM Conference on Electronic Commerce, EC'07 - San Diego, CA, United States
Duration: Jun 11 2007Jun 15 2007

Publication series

NameEC'07 - Proceedings of the Eighth Annual Conference on Electronic Commerce


Conference8th ACM Conference on Electronic Commerce, EC'07
Country/TerritoryUnited States
CitySan Diego, CA


  • Approximation algorithms
  • Pricing
  • Virtual valuations

ASJC Scopus subject areas

  • Management of Technology and Innovation
  • Marketing
  • Computer Networks and Communications
  • Computer Science Applications


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