Abstract
We consider an auction in which a seller invites potential buyers to a sealed-bid first-price auction, without disclosing to the buyers the number of extended invitations. In the presence of a fixed invitation cost for each invited bidder, the whole auction can be described as a game, where the set of players consists of all bidders together with the seller. In a setting with fully observable common values we show the existence of a Nash equilibrium in mixed strategies. In this equilibrium, the seller should invite precisely one or two potential buyers with certain probabilities, and each invited buyer should place a randomized bid according to a certain distribution.
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