The Optimal Allocation of Prizes in Contests
We study a contest with multiple (not necessarily equal) prizes. Contestants have private information about an ability parameter that affects their costs of bidding. The contestant with the highest bid wins the first prize, the contestant with the second-highest bid wins the second prize, and so on until all the prizes are allocated. All contestants incur their respective costs of bidding. The contest's designer maximizes the expected sum of bids. Our main results are: 1) We display bidding equlibria for any number of contestants having linear, convex or concave cost functions, and for any distribution of abilities. 2) If the cost functions are linear or concave, then, no matter what the distribution of abilities is, it is optimal for the designer to allocate the entire prize sum to a single ''first'' prize. 3) We give a necessary and sufficient conditions ensuring that several prizes are optimal if contestants have a convex cost function.
|Date of creation:||14 Jul 1999|
|Date of revision:|
|Note:||We wish to thank Karsten Fieseler, Martin Hellwig, Roman Inderst, Philippe Jehiel, Holger Mueller, Georg Noeldeke and Jan Vleugels for helpful comments. Both authors are grateful for financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim.|
|Contact details of provider:|| Postal: D-68131 Mannheim|
Phone: (49) (0) 621-292-2547
Fax: (49) (0) 621-292-5594
Web page: http://www.sfb504.uni-mannheim.de/
More information through EDIRC
Web page: http://www.sfb504.uni-mannheim.de
|Order Information:|| Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- James J. Anton & Dennis A. Yao, 1992. "Coordination in Split Award Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 681-707.
- Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 675-689.
- Vijay Krishna & John Morgan, 1994.
"An Analysis of the War of Attrition and the All-Pay Auction,"
Game Theory and Information
- 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.
- Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
- Edward P. Lazear & Sherwin Rosen, 1979.
"Rank-Order Tournaments as Optimum Labor Contracts,"
NBER Working Papers
0401, National Bureau of Economic Research, Inc.
- Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-90, September.
- Arye L. Hillman & John G. Riley, 1987.
"Politically Contestable Rents and Transfers,"
UCLA Economics Working Papers
452, UCLA Department of Economics.
- Sherwin Rosen, 1985.
"Prizes and Incentives in Elimination Tournaments,"
NBER Working Papers
1668, National Bureau of Economic Research, Inc.
- Riley, John G & Samuelson, William F, 1981.
American Economic Review,
American Economic Association, vol. 71(3), pages 381-92, June.
- Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
- 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.
- Jerry R. Green & Nancy L. Stokey, 1982.
"A Comparison of Tournaments and Contracts,"
NBER Working Papers
0840, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- Glazer, Amihai & Hassin, Refael, 1988. "Optimal Contests," Economic Inquiry, Western Economic Association International, vol. 26(1), pages 133-43, January.
- 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.
- 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.
- 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.
- Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
- Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
When requesting a correction, please mention this item's handle: RePEc:xrs:sfbmaa:99-75. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carsten Schmidt)
If references are entirely missing, you can add them using this form.