Multidimensional mechanism design for auctions with externalities

In an auction with externalities, a buyer's type is multidimensional and sp ecifies the payoff he would get for each of the Nf I possible outcomes: the seller keeps the object or buyer i (i = I,..., N) gets the object. We prov ide a characterization of multidimensional incentive compatible mechanisms similar to that For one-dimensional mechanisms. Although reservation utilit ies are endogenous and type-dependent, the participation constraint is bind ing for only one "critical" type. A main difficulty in a multidimensional s etting is the "integrability" condition. We present a geometric characteriz ation for discontinuous conservative: vector fields. In auctions where the buyers. submit scalar bids and the seller transfers the object to one of th e buyers for sure, a second-prise auction maximizes revenue. With two buyer s, this auction remains optimal even if the seller can set a reservation pr ice. Journal of Economic Literature Classification Numbers: C7, C72, (C) 19 99 Academic Press.