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Optimal Seedings in Elimination Tournaments

Author

Listed:
  • Groh, Christian
  • Moldovanu, Benny
  • Sela, Aner
  • Sunde, Uwe

Abstract

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction where the winner gets the right to compete at the next round. Equilibrium efforts are in mixed strategies, yielding rather complex play dynamics: the endogenous win probabilities in each match depend on the outcome of other matches through the identity of the expected opponent in the next round. The designer can seed the competitors according to their ranks. For tournaments with four players we find optimal seedings with respect to three different criteria: 1) maximization of total effort in the tournament; 2) maximization of the probability of a final among the two top ranked teams; 3) maximization of the win probability for the top player. In addition, we find the seedings ensuring that higher ranked players have a higher probability to win the tournament. Finally, we compare the theoretical predictions with data from NCAA basketball tournaments.

Suggested Citation

  • Groh, Christian & Moldovanu, Benny & Sela, Aner & Sunde, Uwe, 2003. "Optimal Seedings in Elimination Tournaments," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 140, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    • Handle: RePEc:trf:wpaper:140
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    References listed on IDEAS

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    1. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
    2. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
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    5. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-545, October.
    6. Klaassen, Franc J. G. M. & Magnus, Jan R., 2003. "Forecasting the winner of a tennis match," European Journal of Operational Research, Elsevier, vol. 148(2), pages 257-267, July.
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    8. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    9. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
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    More about this item

    Keywords

    Elimination tournaments; Seedings; All-Pay Auctions;

    JEL classification:

    • 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
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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