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Optimal Auction Design for Multiple Objects with Externalities

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  • Vasiliki Skreta

Abstract

In this paper we characterize the optimal allocation mechanism for $N$ objects, (permits), to $I$ potential buyers, (firms). Firms' payoffs depend on their costs, the costs of competitors and on the final allocation of the permits, allowing for externalities, substitutabilities and complementarities. Firms' cost parameter is private information and is independently distributed across firms. Externalities are type dependent. This has two consequences: first, even though the private information of each firm is one dimensional (its cost), an allocation's virtual valuation (the natural generalization of the virtual valuation introduced in (Myerson (1981) depends on the cost parameters of all firms. Second, the "critical" type of each buyer, (the type for which participation constraint binds) is not exogenously given but depends on the particular mechanism selected. This is not as in the papers by Jehiel, Moldovanu and Stacchetti 1996, 2001, and makes the characterization of the optimum intricate, since the objective function is altered. However, the feasibility constraints remain tractable, which makes the use of variational methods possible. A further consequence of having type-dependent externalities, which does not arise in the previous work, is that not only payments, but also the revenue maximizing allocation is different from the optimum derived without taking into account the existence of externalities. Our model captures key features of many important multi-object allocation problems like the allocation of time slots for TV commercials, landing slots in airports, privatization and firm takeovers

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series UCLA Economics Online Papers with number 345.

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Date of creation: 28 Jan 2005
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Handle: RePEc:cla:uclaol:345

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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. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
  3. repec:att:wimass:9008 is not listed on IDEAS
  4. Dana, James Jr. & Spier, Kathryn E., 1994. "Designing a private industry : Government auctions with endogenous market structure," Journal of Public Economics, Elsevier, vol. 53(1), pages 127-147, January.
  5. Gale, Ian, 1990. "A multiple-object auction with superadditive values," Economics Letters, Elsevier, vol. 34(4), pages 323-328, December.
  6. Armstrong, Mark, 2000. "Optimal Multi-object Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 455-81, July.
  7. repec:wop:humbsf:2000-72 is not listed on IDEAS
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Cited by:
  1. Jehiel, Philippe & Moldovanu, Benny, 2006. "Allocative and Informational Externalities in Auctions and Related Mechanisms," CEPR Discussion Papers 5558, C.E.P.R. Discussion Papers.
  2. Kaplan, Todd R & Zamir, Shmuel, 2014. "Advances in Auctions," MPRA Paper 54656, University Library of Munich, Germany.
  3. Kumru, Cagri & Yektas, Hadi, 2008. "Optimal Multi-Object Auctions with Risk Averse Buyers," MPRA Paper 7575, University Library of Munich, Germany.

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