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The Allocation of a Prize

  • Pradeep K. Dubey
  • Siddhartha Sahi

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.

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Date of creation: 13 Apr 2012
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Handle: RePEc:cla:levarc:786969000000000402
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  1. Broecker, Thorsten, 1990. "Credit-Worthiness Tests and Interbank Competition," Econometrica, Econometric Society, vol. 58(2), pages 429-52, March.
  2. Green, Jerry & Stokey, Nancy, 1983. "A Comparison of Tournaments and Contracts," Scholarly Articles 3203644, Harvard University Department of Economics.
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  12. Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
  13. 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.
  14. Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,... or A, B, C?," Levine's Working Paper Archive 814577000000000361, David K. Levine.
  15. 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.
  16. 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.
  17. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
  18. 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.
  19. Nti, Kofi O, 1999. " Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-30, March.
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