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Multidimensional Mechanism Design for Auctions with Externalities

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  • Jehiel, Phillipe

    ()
    (ENPC, CERAS, Paris and UCL, London)

  • Moldovanu, Benny

    ()
    (Department of Economics, University of Mannheim, Germany)

  • Stacchetti, E.

    (University of Michigan)

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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 504, Universit├Ąt Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 97-04.

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Length: 0 pages
Date of creation: 01 Jan 1997
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Handle: RePEc:xrs:sfbmaa:97-04

Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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References

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  1. ehiel, Philippe & Benny Moldovanu & Ennio Stacchetti, 1994. "How (not) to sell nuclear weapons," Discussion Paper Serie B 288, University of Bonn, Germany.
  2. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
  3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  4. Champsaur, Paul & Rochet, Jean-Charles, 1989. "Multiproduct Duopolists," Econometrica, Econometric Society, vol. 57(3), pages 533-57, May.
  5. McAfee, R Preston & McMillan, John & Whinston, Michael D, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 371-83, May.
  6. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  7. Spence, A Michael, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," Review of Economic Studies, Wiley Blackwell, vol. 47(5), pages 821-41, October.
  8. Steven Matthews & John Moore, 1985. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Discussion Papers 661, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Wilson, Robert, 1991. "Multiproduct Tariffs," Journal of Regulatory Economics, Springer, vol. 3(1), pages 5-26, March.
  10. 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.
  11. Palfrey, Thomas R, 1983. "Bundling Decisions by a Multiproduct Monopolist with Incomplete Information," Econometrica, Econometric Society, vol. 51(2), pages 463-83, March.
  12. Laffont, Jean-Jacques & Tirole, Jean, 1990. "The regulation of multiproduct firms : Part I: Theory," Journal of Public Economics, Elsevier, vol. 43(1), pages 1-36, October.
  13. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  14. Wilson, Robert, 1991. "Erratum [Multiproduct Tariffs]," Journal of Regulatory Economics, Springer, vol. 3(2), pages 211-12, June.
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