Chapter

Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 50-62

Sequential Item Pricing for Unlimited Supply

  • Maria-Florina BalcanAffiliated withCollege of Computing, Georgia Institute of Technology
  • , Florin ConstantinAffiliated withCollege of Computing, Georgia Institute of Technology

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Abstract

We study prior-free revenue maximization for a seller with unlimited supply of n item types facing m myopic buyers present for \(k\!<\!\log n\) days. We show that a certain randomized schedule of posted prices has an approximation factor of \(O(\frac{\log m + \log n}{k})\). This algorithm relies on buyer valuations having hereditary maximizers, a novel natural property satisfied for example by gross substitutes valuations. We obtain a matching lower bound with multi-unit valuations. In light of existing results [2], k days can thus improve the approximation by a Θ(k) factor. We also provide a posted price schedule with the same factor for positive affine allocative externalities, despite an increase in the optimal revenue.