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Multidimensional Mechanism Design for Auctions with Externalities

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  • Moldovanu, Benny
  • Jehiel, Philippe
  • Stacchetti, Ennio

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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Moldovanu, Benny & Jehiel, Philippe & Stacchetti, Ennio, 1997. "Multidimensional Mechanism Design for Auctions with Externalities," Papers 97-04, Sonderforschungsbreich 504.
  • Handle: RePEc:mnh:spaper:16261
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    References listed on IDEAS

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    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. Leonard J. Mirman & David Sibley, 1980. "Optimal Nonlinear Prices for Multiproduct Monopolies," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 659-670, Autumn.
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