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Multidimensional Mechanism Design for Auctions with Externalities

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  • Jehiel, Philippe
  • Moldovanu, Benny
  • 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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 85 (1999)
Issue (Month): 2 (April)
Pages: 258-293

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Handle: RePEc:eee:jetheo:v:85:y:1999:i:2:p:258-293

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-29, September.
  2. 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.
  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. Wilson, Robert, 1991. "Erratum [Multiproduct Tariffs]," Journal of Regulatory Economics, Springer, vol. 3(2), pages 211-12, June.
  5. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-67, March.
  6. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
  7. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  8. Champsaur, Paul & Rochet, Jean-Charles, 1989. "Multiproduct Duopolists," Econometrica, Econometric Society, vol. 57(3), pages 533-57, May.
  9. Wilson, Robert, 1991. "Multiproduct Tariffs," Journal of Regulatory Economics, Springer, vol. 3(1), pages 5-26, March.
  10. Palfrey, Thomas R, 1983. "Bundling Decisions by a Multiproduct Monopolist with Incomplete Information," Econometrica, Econometric Society, vol. 51(2), pages 463-83, March.
  11. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  12. 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.
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