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We investigate the class of single-round, sealed-bid auctions for a set of identical items to bidders who each desire one unit. We adopt the worst-case competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal single-price sale of least two items. In this paper, we first derive an optimal auction for three items, answering an open question from  . Second, we show that the form of this auction is independent of the competitive framework used. Third,doi:10.1145/1064009.1064028 dblp:conf/sigecom/HartlineM05 fatcat:zg7uigoimjgjnezen4fndzmfpe