Optimal Auction Design For Multiple Objects with Externalities
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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- Gale, Ian, 1990.
"A multiple-object auction with superadditive values,"
Elsevier, vol. 34(4), pages 323-328, December.
- Gale, I., 1990. "A Multiple-Object Auction With Superadditive Values," Working papers 9008, Wisconsin Madison - Social Systems.
- Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
- Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996.
"How (Not) to Sell Nuclear Weapons,"
American Economic Review,
American Economic Association, vol. 86(4), pages 814-829, September.
- Mark Armstrong, 2000. "Optimal Multi-Object Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 455-481.
- 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.
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