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Optimal Pricing Is Hard

  • Constantinos Daskalakis
  • Alan Deckelbaum
  • Christos Tzamos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We show that computing the revenue-optimal deterministic auction in unit-demand single-buyer Bayesian settings, i.e. the optimal item-pricing, is computationally hard even in single-item settings where the buyer’s value distribution is a sum of independently distributed attributes, or multi-item settings where the buyer’s values for the items are independent. We also show that it is intractable to optimally price the grand bundle of multiple items for an additive bidder whose values for the items are independent. These difficulties stem from implicit definitions of a value distribution. We provide three instances of how different properties of implicit distributions can lead to intractability: the first is a #P-hardness proof, while the remaining two are reductions from the SQRT-SUM problem of Garey, Graham, and Johnson [14]. While simple pricing schemes can oftentimes approximate the best scheme in revenue, they can have drastically different underlying structure. We argue therefore that either the specification of the input distribution must be highly restricted in format, or it is necessary for the goal to be mere approximation to the optimal scheme’s revenue instead of computing properties of the scheme itself.

Keywords

Electronic Commerce Price Problem Optimal Mechanism Revenue Maximization Oracle Access 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Constantinos Daskalakis
    • 1
  • Alan Deckelbaum
    • 2
  • Christos Tzamos
    • 1
  1. 1.MIT, EECS, CSAILUSA
  2. 2.MIT, Math, CSAILUSA

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