The Allocation of a Prize
Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize deterministically to the agent with the highest output, or to all of them with probabilities that are proportional to their outputs. We show that, if there is sufficient diversity in agents' skills relative to the noise on output, then the proportional prize will, in a precise sense, elicit more output on average, than the deterministic prize. Indeed, assuming agents know each others' skills (the complete information case), this result holds when any Nash equilibrium selection, under the proportional prize, is compared with any individually rational selection under the deterministic prize. When there is incomplete information, the result is still true but now we must restrict to Nash selections for both prizes. We also compute the optimal scheme, from among a natural class of probabilistic schemes, for awarding the prize; namely that which elicits maximal effort from the agents for the least prize. In general the optimal scheme is a monotonic step function which lies "between" the proportional and deterministic schemes. When the competition is over small fractional increments, as happens in the presence of strong contestants whose base levels of production are high, the optimal scheme awards the prize according to the "log of the odds," with odds based upon the proportional prize.
(This abstract was borrowed from another version of this item.)
References listed on IDEAS
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.:
- Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
- Green, Jerry & Stokey, Nancy, 1983.
"A Comparison of Tournaments and Contracts,"
3203644, Harvard University Department of Economics.
- Che, Yeon-Koo & Gale, Ian L, 1998.
"Caps on Political Lobbying,"
American Economic Review,
American Economic Association, vol. 88(3), pages 643-51, June.
- Baye, M.R. & Kovenock, D. & De Vries, C.G., 1992.
"Rigging the Lobbying Process: An Application of the All- Pay Auction,"
9-92-2, Pennsylvania State - Department of Economics.
- Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-94, March.
- Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "Rigging The Lobbying Process: An Application Of The All- Pay Auction," Purdue University Economics Working Papers 1002, Purdue University, Department of Economics.
- Rowley, Charles K, 1991. " Gordon Tullock: Entrepreneur of Public Choice," Public Choice, Springer, vol. 71(3), pages 149-69, September.
- Sherwin Rosen, 1985.
"Prizes and Incentives in Elimination Tournaments,"
NBER Working Papers
1668, National Bureau of Economic Research, Inc.
- Ellingsen, T., 1990.
"Strategic Buyers and the Social Cost of Monopoly,"
05-90, Norwegian School of Economics and Business Administration-.
- Arye L. Hillman & John G. Riley, 1987.
"Politically Contestable Rents and Transfers,"
UCLA Economics Working Papers
452, UCLA Department of Economics.
- Fang, Hanming, 2002. " Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-71, September.
- 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.
- 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.
- Dubey, Pradeep & Haimanko, Ori, 2003.
"Optimal scrutiny in multi-period promotion tournaments,"
Games and Economic Behavior,
Elsevier, vol. 42(1), pages 1-24, January.
- Pradeep Dubey & Ori Haimanko, 2000. "Optimal Scrutiny in Multi-Period Promotion Tournaments," Cowles Foundation Discussion Papers 1254, Cowles Foundation for Research in Economics, Yale University.
- Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. " The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-80, December.
- Pradeep Dubey & John Geanakoplos, 2009.
"Grading Exams: 100, 99, 98,... or A, B, C?,"
Levine's Working Paper Archive
814577000000000361, David K. Levine.
- Che, Yeon-Koo & Gale, Ian, 1997. " Rent Dissipation When Rent Seekers Are Budget Constrained," Public Choice, Springer, vol. 92(1-2), pages 109-26, July.
- Benny Moldovanu & Aner Sela, 2001.
"The Optimal Allocation of Prizes in Contests,"
American Economic Review,
American Economic Association, vol. 91(3), pages 542-558, June.
- M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
- Pradeep Dubey & John Geanakoplos, 2005.
"Grading in Games of Status: Marking Exams and Setting Wages,"
Cowles Foundation Discussion Papers
1544, Cowles Foundation for Research in Economics, Yale University.
- Pradeep Dubey & John Geanakoplos, 2005. "Grading in Games of Status: Marking Exams and Setting Wages," Cowles Foundation Discussion Papers 1544, Cowles Foundation for Research in Economics, Yale University, revised Dec 2005.
- Nti, Kofi O, 1999. " Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-30, March.
- Glazer, Amihai & Hassin, Refael, 1988. "Optimal Contests," Economic Inquiry, Western Economic Association International, vol. 26(1), pages 133-43, January.
- Edward P. Lazear & Sherwin Rosen, 1979.
"Rank-Order Tournaments as Optimum Labor Contracts,"
NBER Working Papers
0401, National Bureau of Economic Research, Inc.
- 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.
When requesting a correction, please mention this item's handle: RePEc:cla:levarc:786969000000000402. 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: (David K. Levine)
If references are entirely missing, you can add them using this form.