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Multidimensional mechanism design for auctions with externalities. (English) Zbl 1028.91539
Summary: In an auction with externalities, a buyer’s type is multidimensional and specifies the payoff he would get for each of the \(N+ 1\) possible outcomes: the seller keeps the object or buyer \(i\) \((i= 1,\dots, N)\) gets the object. We provide a characterization of multidimensional incentive compatible mechanisms similar to that for one-dimensional mechanisms. Although reservation utilities are endogenous and type-dependent, the participation constraint is binding for only one “critical” type. A main difficulty in a multidimensional setting is the “integrability” condition. We present a geometric characterization for discontinuous conservative vector fields. In auctions where the buyers submit scalar bids and the seller transfers the object to one of the buyers for sure, a second-price auction maximizes revenue. With two buyers, this auction remains optimal even if the seller can set a reservation price.

MSC:
91B26 Auctions, bargaining, bidding and selling, and other market models
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