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Round-Robin Tournaments with Effort Constraints

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  • Erez, Eyal
  • Sela, Aner
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    Abstract

    We study a round-robin tournament with n symmetric players where in each of the n-1 stages each of the players competes against a different player in the Tullock contest. Each player has a limited budget of effort that decreases within the stages proportionally to the effort he exerted in the previous stages. We show that when the prize for winning (value of winning) is equal between the stages, a player's effort is weakly decreasing over the stages. We also show how the contest designer can influence the players' allocation of effort by changing the distribution of prizes between the stages. In particular, we analyze the optimal distribution of prizes over the stages that balance the effort allocation such that a player exerts the same effort over the different stages. In addition, we analyze the distribution of prizes over the stages that maximizes the players' expected total effort.

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    Bibliographic Info

    Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8021.

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    Date of creation: Sep 2010
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    Handle: RePEc:cpr:ceprdp:8021

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    Related research

    Keywords: effort Constraints; Round-Robin Tournaments; Tullock Contests;

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    References

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    1. Konrad, Kai A., 2004. "Bidding in hierarchies," European Economic Review, Elsevier, vol. 48(6), pages 1301-1308, December.
    2. Moldovanu, Benny & Sela, Aner, 2002. "Contest Architecture," Sonderforschungsbereich 504 Publications, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim 02-06, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    3. Rick Harbaugh & Tilman Klumpp, 2004. "Early Round Upsets and Championship Blowouts," Working Papers, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy 2004-09, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
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    7. Wärneryd, Karl, 1997. "Distributional Conflict and Jurisdictional Organization," Working Paper Series in Economics and Finance 173, Stockholm School of Economics.
    8. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers, University of Pittsburgh, Department of Economics 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
    9. J. Atsu Amegashie & C. Bram Cadsby & Yang Song, 2005. "Competitive Burnout: Theory and Experimental Evidence," Working Papers, University of Guelph, Department of Economics and Finance 0507, University of Guelph, Department of Economics and Finance.
    10. Sherwin Rosen, 1985. "Prizes and Incentives in Elimination Tournaments," NBER Working Papers 1668, National Bureau of Economic Research, Inc.
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    12. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, Springer, vol. 29(1), pages 1-24, September.
    13. Dmitry Ryvkin & Andreas Ortmann, 2008. "The Predictive Power of Three Prominent Tournament Formats," Management Science, INFORMS, INFORMS, vol. 54(3), pages 492-504, March.
    14. Dmitry Ryvkin, 2011. "Fatigue in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(4), pages 1011-1041, December.
    15. Christopher Ferrall & Anthony A. Smith, 1999. "A Sequential Game Model Of Sports Championship Series: Theory And Estimation," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 704-719, November.
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    17. Che, Yeon-Koo & Gale, Ian, 1997. " Rent Dissipation When Rent Seekers Are Budget Constrained," Public Choice, Springer, Springer, vol. 92(1-2), pages 109-26, July.
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