Cr¨¦mer and McLean  and McAfee and Reny  showed that, in "nearly all auctions", the seller can offer a mechanism that obtains full rent extraction. The mechanism designed by Cr¨¦mer and McLean differs from standard procedures in several respects. Notably, (a) bidders are required to buy "lotteries" in order to partecipate at the auction; (b) bidders are treated non-anonymously, in the sense that different bidders are given different strategic options; (c) the bidders' payments to the seller depend not only on the bids but also on some other "actions" taken by the bidders. In this paper, I keep (a) and (b), and impose that ¡ª like in the "standard model of auctions" ¡ª the bidders' payments to the seller depend on the bids alone. I find that the full-surplus extraction result no longer holds: There are "open sets" of auctions where the full extraction is not possible.
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