Sequential item pricing for unlimited supply
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A common challenge faced by sellers is to explore and exploit, in limited time, buyers' willingness to pay. We propose distribution-free revenue maximization techniques for a seller with unlimited supply of n item types facing m myopic buyers present for k < n days. We highlight the power of linear uniform prices (i.e. equal item prices) for buyer valuations with hereditary maximizers (HM), e.g. multi-unit or gross substitutes valuations. In particular, we present a non-increasing, randomized, schedule of k linear uniform prices with expected revenue within a log[k](mn) factor of optimal given HM valuations. Our result improves by a log k factor 's approximation for general valuations and one-shot prices, and does not go through even for submodular valuations. We also consider influences (in the form of allocative externalities) be- tween buyers with HM valuations. We provide a rather general model of positive influence of other buyers' ownership of some items on a buyer's valuation. For affine, submodular externalities, we present an influence- and-exploit  marketing strategy based on our algorithm for private HM valuations. This strategy preserves our log[k](mn) approximation factor, despite an affine increase (due to externalities) in the optimum revenue.