Multidimensional Mechanism Design for Auctions with Externalities

Philippe Jehiel (), Benny Moldovanu () and E. Stacchetti
Additional contact information
E. Stacchetti: University of Michigan, Postal: Michigan

No 97-04, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim, Sonderforschungsbereich 504, University of Mannheim

Abstract: In our framework, when a buyer does not obtain the auctioned object, he is no longer indifferent about the identity of the winner (i.e., eyternal effects are present). Buyer i's preferences are characterized by an N-dimensional vector t^i = (t1^i, t2^i,..,tN^i). The coordinate ti^i can be interpreted as the usual "private value" of player i, while each other coordinate tj^i represents i's total payoff should j get the object. In this framework, we characterize incentive-compatible and individually-rational mechanisms, and look at second price auctions (which, under some conditions, maximize the seller's revenue). Any incentive combatible mechanism induces a conditional probability assignement vector field which is conservative. A useful geometric property of conservative vector fields is used for the derivation of a differential equation which determines equilibrium bids. Finally, we show that exclusion (i.e., the announcement of a reservation price such that a measure can never get the object) is not necessarilly optimal for the seller. This contrasts with Armstrong's (Econometrica, 1995) insight about the optimality of exclusion in another multidimensional setting.

Pages: 0 pages
Date: 1997-01-01
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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Related works:
Journal Article: Multidimensional Mechanism Design for Auctions with Externalities (1999)
Working Paper: Multidimensional Mechanism Design for Auctions with Externalities (1997)
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