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The monopolist's theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson 8: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer 1: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents' valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition.
Hartline et al. (Mon,) studied this question.
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