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.:
- Pradeep Dubey & John Geanakoplos, 2009.
"Grading Exams: 100, 99, 98,...or A, B, C?,"
Cowles Foundation Discussion Papers
1710, Cowles Foundation for Research in Economics, Yale University.
- Green, Jerry & Stokey, Nancy, 1983.
"A Comparison of Tournaments and Contracts,"
3203644, Harvard University Department of Economics.
- 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.
- Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
- Rowley, Charles K, 1991. " Gordon Tullock: Entrepreneur of Public Choice," Public Choice, Springer, vol. 71(3), pages 149-69, September.
- 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, 1989.
"Politically Contestable Rents And Transfers,"
Economics and Politics,
Wiley Blackwell, vol. 1(1), pages 17-39, 03.
- 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., 1992. "Rigging the Lobbying Process: An Application of the All- Pay Auction," Papers 9-92-2, Pennsylvania State - Department of Economics.
- 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.
- Lazear, Edward P & Rosen, Sherwin, 1981.
"Rank-Order Tournaments as Optimum Labor Contracts,"
Journal of Political Economy,
University of Chicago Press, vol. 89(5), pages 841-64, October.
- M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
- Sherwin Rosen, 1985.
"Prizes and Incentives in Elimination Tournaments,"
NBER Working Papers
1668, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Yeon-Koo Che & Ian Gale, 1998.
"Caps on Political Lobbying,"
- Moldovanu, Benny & Sela, Aner, 1999.
"The Optimal Allocation of Prizes in Contests,"
Sonderforschungsbereich 504 Publications
99-75, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- 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.
- 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.
- 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.
- Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
- Nti, Kofi O, 1999. " Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-30, March.
- 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.
- Glazer, Amihai & Hassin, Refael, 1988. "Optimal Contests," Economic Inquiry, Western Economic Association International, vol. 26(1), pages 133-43, January.
- 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.
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 you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.