Parametric digital auctions

We study revenue maximization for digital auctions, where there are infinitely many copies of a good for sale. There are n buyers, each of whom is interested in obtaining one copy of the good. The buyers' private valuations are drawn from a joint distribution vec{F}. The seller does not know this distribution. The only information that she has are the mean ui and variance σi2 of each buyer i's marginal distribution Fi. We call such auctions parametric auctions. We construct a deterministic parametric auction that, for a wide class of distributions, guarantees a constant fraction of the optimal revenue achievable when the seller precisely knows the distribution F. Furthermore, our auction is a posted price mechanism and it is maximin optimal among all such mechanisms. That is, it is the posted price mechanism that maximizes revenue in the worst case over an adversarial choice of the distribution.

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