  Many auction settings implicitly or explicitly require that bidders are
treated equally ex-ante. This may be because discrimination is philosophically
or legally impermissible, or because it is practically difficult to implement
or impossible to enforce. We study so-called {\em anonymous} auctions to
understand the revenue tradeoffs and to develop simple anonymous auctions that
are approximately optimal.
  We consider digital goods settings and show that the optimal anonymous,
dominant strategy 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 O(n) to the optimal revenue in the worst case (or O(log n) 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 O(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 and build on this mechanism to extend our results to
m-unit auctions and sponsored search.
