Auctions that select core allocations with respect to reported values generate competitive levels of sales revenues at equilibrium and limit bidder incentives to use shills. Among core-selecting auctions, the ones that minimize seller revenues also maximize incentives for truthful reporting, produce the Vickrey outcome when that lies in the core and, in contrast to the Vickrey auction, and create no incentive for a seller to exclude qualified bidders. Core-selecting auctions are related to and share properties with stable matching mechanisms.
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