Sequential item pricing for unlimited supply

Authors:
Maria-Florina Balcan;Florin Constantin
Affiliations:
College of Computing, Georgia Institute of Technology;College of Computing, Georgia Institute of Technology
Venue:
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Year:
2010

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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 n days. We show that a certain randomized schedule of posted prices has an approximation factor of O(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.