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The Optimal Allocation of Prizes in Contests

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Author Info
Benny Moldovanu
Aner Sela

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Abstract

We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single "first" prize. When cost functions are convex, several positive prizes may be optimal.

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Publisher Info
Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 91 (2001)
Issue (Month): 3 (June)
Pages: 542-558
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Handle: RePEc:aea:aecrev:v:91:y:2001:i:3:p:542-558

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  1. Edward P. Lazear & Sherwin Rosen, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Baye, M.R. & Kovenock, D. & De Vries, C., 1992. "The All-Pay Auction with Complete Information," Papers 8-92-1, Pennsylvania State - Department of Economics.
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  3. Anton, James J & Yao, Dennis A, 1992. "Coordination in Split Award Auctions," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 681-707, May. [Downloadable!] (restricted)
  4. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May. [Downloadable!] (restricted)
  5. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June. [Downloadable!] (restricted)
  6. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-15, September. [Downloadable!] (restricted)
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  7. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 1992. "It takes two to tango: Equilibria in a model of sales," Games and Economic Behavior, Elsevier, vol. 4(4), pages 493-510, October. [Downloadable!] (restricted)
  8. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  9. Glazer, Amihai & Hassin, Refael, 1988. "Optimal Contests," Economic Inquiry, Oxford University Press, vol. 26(1), pages 133-43, January.
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  11. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March. [Downloadable!] (restricted)
  12. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-92, June. [Downloadable!] (restricted)
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  13. Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March. [Downloadable!] (restricted)
  14. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September. [Downloadable!] (restricted)
  15. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics. [Downloadable!]
  16. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February. [Downloadable!] (restricted)
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  17. Knoeber, Charles R & Thurman, Walter N, 1994. "Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production," Journal of Labor Economics, University of Chicago Press, vol. 12(2), pages 155-79, April. [Downloadable!] (restricted)
  18. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November. [Downloadable!] (restricted)
  19. Wilson, Robert, 1979. "Auctions of Shares," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 675-89, November. [Downloadable!] (restricted)
  20. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-64, June. [Downloadable!] (restricted)
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  21. Wright, Brian Davern, 1983. "The Economics of Invention Incentives: Patents, Prizes, and Research Contracts," American Economic Review, American Economic Association, vol. 73(4), pages 691-707, September. [Downloadable!] (restricted)
  22. Ehrenberg, Ronald G & Bognanno, Michael L, 1990. "Do Tournaments Have Incentive Effects?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1307-24, December. [Downloadable!] (restricted)
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  23. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-89, March. [Downloadable!] (restricted)
  24. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January. [Downloadable!] (restricted)
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