Auctioning with Aspirations: Keep Them Low (Enough)
In an auction with a buy price, a seller offers bidders the opportunity to forgo competing in an auction by transacting immediately at a pre-specified fixed price. If a seller has aspirations in the form of a reference price that depends upon the auction's reserve price and buy price, she does best to keep her aspirations sufficiently low by designing a no-reserve auction with a buy price low enough that some bidder types would exercise it with positive probability in equilibrium. The seller is indifferent between the auction component of her mechanism being a first- or second-price auction.
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