Optimal Parametric Auctions

We study the problem of profit maximization in auctions of one good where the buyers' valuations are drawn from independent distributions. When these distributions are known to the seller, Myerson's optimal auction is a well-known mechanism for maximizing revenue. In many cases, however, the seller may not know the buyers' distributions. We propose an alternative model where the seller only knows the mean and the variance of each distribution. We call parametric an auction whose mechanism only uses these parameters. We construct parametric auctions both when the seller only has one copy of the good to sell, and when she has an infinite number of identical copies (i.e., when the good is digital). For a very large class of distributions, including (but not limited to) distributions with a monotone hazard rate, our auctions achieve a constant fraction of the revenue of Myerson's auction. When the seller has absolutely no knowledge about the distributions, it is well known that no auction can achieve a constant fraction of the optimal revenue when the players are not identically distributed. Our parametric model gives the seller a small amount of extra information, allowing her to construct auctions for which (1) no two bidders need to be drawn from identical distributions and (2) the revenue obtained is a constant fraction of the revenue in Myerson's optimal auction