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Optimal Tournaments

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  • Drugov, Mikhail
  • Ryvkin, Dmitry

Abstract

We study the optimal allocation of prizes and comparative statics of multi-prize rank-order tournaments. For a principal allocating a fixed budget, we show that the winner-take-all (WTA) prize schedule is optimal when the distribution of noise has an increasing failure rate (IFR). For noise distributions with unimodal failure rates the optimal prize allocation moves closer to WTA as the noise distribution becomes smaller in the convex transform order. We also identify a natural ordering of prize schedules by how closely they approximate the WTA schedule and show that for log-concave noise distributions the equilibrium effort is monotone in this order. The impact of noise intensity on equilibrium effort is captured by the dispersive order.

Suggested Citation

  • Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Optimal Tournaments," CEPR Discussion Papers 12368, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:12368
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    References listed on IDEAS

    as
    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    3. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    4. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    5. Loukas Balafoutas & E. Glenn Dutcher & Florian Lindner & Dmitry Ryvkin, 2017. "The Optimal Allocation Of Prizes In Tournaments Of Heterogeneous Agents," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 461-478, January.
    6. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    7. Edward P. Lazear, 1999. "Personnel Economics: Past Lessons and Future Directions," NBER Working Papers 6957, National Bureau of Economic Research, Inc.
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    More about this item

    Keywords

    Tournament; Optimal allocation of prizes; Unimodality; Failure rate; Comparative statics; Dispersive order; Convex transform order;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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