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The Allocation of a Prize (Expanded)

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  • Pradeep Dubey

    ()
    (Department of Economics, Stony Brook University)

  • Siddhartha Sah

    (Department of Mathematics, Rutgers University, New Brunswick, New Jersey)

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    Abstract

    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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    File URL: http://www.stonybrook.edu/economics/research/papers/2012/paper2012.pdf
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    Bibliographic Info

    Paper provided by Stony Brook University, Department of Economics in its series Department of Economics Working Papers with number 12-02.

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    Date of creation: Mar 2012
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    Handle: RePEc:nys:sunysb:12-02

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    References

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    17. Moldovanu, Benny & Sela, Aner, 1999. "The Optimal Allocation of Prizes in Contests," Sonderforschungsbereich 504 Publications 99-75, Sonderforschungsbereich 504, Universit├Ąt Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    18. 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.
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