Anonymous Auctions Maximizing Revenue.

Auctions like sponsored search often implicitly or explicitly require that bidders are treated fairly. This may be because large bidders have market power to negotiate equal treatment, because small bidders are difficult to identify, or for many other reasons. We study so-called anonymous auctions to understand the revenue tradeoffs and to develop simple anonymous auctions that are approximately optimal. We begin with the canonical digital goods setting and show that the optimal anonymous, ex-post incentive compatible auction has an intuitive structure -- imagine that bidders are randomly permuted before the auction, then infer a posterior belief about bidder i's valuation from the values of other bidders and set a posted price that maximizes revenue given this posterior. We prove that no anonymous mechanism can guarantee an approximation better than $$\\varTheta n$$﾿n to the optimal revenue in the worst case or $$\\varTheta \\log n$$﾿logn for regular distributions and that even posted price mechanisms match those guarantees. Understanding that the real power of anonymous mechanisms comes when the auctioneer can infer the bidder identities accurately, we show a tight $$\\varTheta k$$﾿k approximation guarantee when each bidder can be confused with at most k \"higher types\". Moreover, we introduce a simple mechanism based on n target prices that is asymptotically optimal. Finally, we return to our original motivation and build on this mechanism to extend our results to m-unit auctions and sponsored search.