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The Predictive Power of Noisy Round-Robin Tournaments

Author

Listed:
  • Dmitry Ryvkin
  • Andreas Ortmann

Abstract

The round-robin tournament format for N players is a scheme that matches players with one another in all possible N(N - 1)/2 pairwise comparisons. A noisy round-robin tournament adds the possibility of upsets, or noise, and hence reduces the power of the tournament to reveal the true ranking of the players. In this article we study theoretically (analytically and by way of computational simulations) the predictive power of noisy round-robin tournaments for three prominent distributions of players’ abilities, as a function of the level of noise and the number of players. At first sight, some of our results (e.g., non-monotonicity as a function of the number of players N, which makes some ranges of N non-optimal) are quite counterintuitive but should be of help to a tournament designer who tries to maximize, or maybe minimize, the probability of the best player winning.

Suggested Citation

  • Dmitry Ryvkin & Andreas Ortmann, 2004. "The Predictive Power of Noisy Round-Robin Tournaments," CERGE-EI Working Papers wp236, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
  • Handle: RePEc:cer:papers:wp236
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    File URL: http://www.cerge-ei.cz/pdf/wp/Wp236.pdf
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    References listed on IDEAS

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    1. 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.
    2. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    3. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    4. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    5. Jonathan Levin & Barry Nalebuff, 1995. "An Introduction to Vote-Counting Schemes," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 3-26, Winter.
    6. Dmitry Ryvkin, 2005. "The Predictive Power of Noisy Elimination Tournaments," CERGE-EI Working Papers wp252, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    7. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    8. Knoeber, Charles R & Thurman, Walter N, 1994. "Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production," Journal of Labor Economics, University of Chicago Press, vol. 12(2), pages 155-179, April.
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    Citations

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    Cited by:

    1. Dmitry Ryvkin, 2005. "The Predictive Power of Noisy Elimination Tournaments," CERGE-EI Working Papers wp252, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Dmitry Ryvkin & Andreas Ortmann, 2006. "Three Prominent Tournament Formats: Predictive Power and Costs," CERGE-EI Working Papers wp303, The Center for Economic Research and Graduate Education - Economics Institute, Prague.

    More about this item

    Keywords

    Round-robin tournaments; Noise; Power distributions; Design economics;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory

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