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The Allocation of a Prize (R)

Author

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  • Pradeep Dubey

    (Center for Game Theory, Department of Economics, Stony Brook University)

  • Siddhartha Sahi

    (Dept. of Mathematics, Rutgers University, New Brunswick)

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.

Suggested Citation

  • Pradeep Dubey & Siddhartha Sahi, 2012. "The Allocation of a Prize (R)," Cowles Foundation Discussion Papers 1858, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1858
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    References listed on IDEAS

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    Cited by:

    1. Pradeep Dubey & Siddhartha Sahi, 2009. "The Allocation of a Prize," Department of Economics Working Papers 09-01, Stony Brook University, Department of Economics.
    2. Aner Sela & Ezra Einy & 0ri Haimanko & Diego Moreno & Avishay Aiche & Benyamin Shitovitz, 2016. "Information Advantage in Common-Value Classic Tullock Contests," Working Papers 1614, Ben-Gurion University of the Negev, Department of Economics.
    3. Pradeep Dubey & Siddhartha Sah, 2012. "The Allocation of a Prize (Expanded)," Department of Economics Working Papers 12-02, Stony Brook University, Department of Economics.
    4. Dubey, Pradeep, 2013. "The role of information in contests," Economics Letters, Elsevier, vol. 120(2), pages 160-163.

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    More about this item

    Keywords

    Deterministic/proportional/optimal prizes; Games of complete/incomplete information; Nash equilibrium; Individually rational strategies;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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