Prior-Independent Optimal Auctions

Abstract

Auctions are widely used in practice. While also extensively studied in the literature, most of the developments rely on the significant common prior assumption. We study the design of optimal prior-independent selling mechanisms: buyers do not have any information about their competitors and the seller does not know the distribution of values, but only a general class it belongs to. Anchored on the canonical model of two buyers with iid values, we analyze a competitive ratio objective, in which the seller attempts to optimize the worst-case fraction of revenues garnered compared to those of an oracle with knowledge of the distribution. We characterize properties of optimal mechanisms, and in turn establish fundamental impossibility results through upper bounds on the maximin ratio. By also deriving lower bounds on the maximin ratio, we are able to crisply characterize the optimal performance for a spectrum of families of distributions. In particular, our results imply that a second price auction is an optimal mechanism when the seller only knows that the distribution of buyers has a monotone non-decreasing hazard rate, and guarantees at least 71.53% of oracle revenues against any distribution within this class. Furthermore, a second price auction is near-optimal when the class of admissible distributions is that of those with non-decreasing virtual values (aka regular). Under this class, it guarantees a fraction of 50% of oracle revenues and no mechanism can guarantee more than 55.6%. Finally, we extend our results to the case of an unknown and adversarially selected number of buyers.