Sequential item pricing for unlimited supply
Maria-Florina Balcan, Florin Constantin

TL;DR
This paper develops dynamic pricing strategies for unlimited supply items over multiple days, achieving near-optimal revenue approximation for buyers with hereditary maximizer valuations and extending to influence-based externalities.
Contribution
It introduces a non-increasing, randomized pricing schedule that improves revenue approximation in dynamic settings and initiates study of externalities in revenue maximization.
Findings
Dynamic pricing schedule achieves O((log m + log n)/k) approximation.
Lower bounds show the approximation factor cannot be significantly improved.
Extends model to include externalities with affine, submodular influence, maintaining approximation guarantees.
Abstract
We investigate the extent to which price updates can increase the revenue of a seller with little prior information on demand. 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. For the static (k = 1) case, Balcan et al. [2] show that one random item price (the same on each item) yields revenue within a \Theta(log m + log n) factor of optimum and this factor is tight. We define the hereditary maximizers property of buyer valuations (satisfied by any multi-unit or gross substitutes valuation) that is sufficient for a significant improvement of the approximation factor in the dynamic (k > 1) setting. Our main result is a non-increasing, randomized, schedule of k equal item prices with expected revenue within a O((log m + log n) / k) factor of optimum for private valuations with hereditary…
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Taxonomy
TopicsAuction Theory and Applications · Consumer Market Behavior and Pricing · Optimization and Search Problems
