On the Competitive Ratio of Online Sampling Auctions

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Abstract

We study online profit-maximizing auctions for digital goods with adversarial bid selection and uniformly random arrivals. Our goal is to design auctions that are constant competitive with $\mathcal{F}^{(2)}$ ; in this sense our model lies at the intersection of prior-free mechanism design and secretary problems. We first give a generic reduction that transforms any offline auction to an online one, with only a loss of a factor of 2 in the competitive ratio; we then present some natural auctions, both randomized and deterministic, and study their competitive ratio; our analysis reveals some interesting connections of one of these auctions with RSOP, which we further investigate in our final section.