In sport tournaments, the rules are presumably structured in a way that any participant cannot benefit by losing instead of winning. We show that tournament systems, consisting of multiple round-robin and knockout tournaments with noncumulative prizes, which are ubiquitous around the world, are generically incentive incompatible. We use our model to discuss potential remedies and applications.
ArrowK. (1963). Social choice and individual values (2nd ed.). New Haven, CT: Yale University Press.
2.
BaumannR.MathesonV. A.HoweC. A. (2010). Anomalies in tournament design: The madness of March madness. Journal of Quantitative Analysis in Sports, 6, 1–9.
3.
BouyssouD. (2004). Monotonicity of ‘ranking by choosing’: A progress report. Social Choice and Welfare, 23, 249–273.
4.
ChenX.DengX.LiuB. J. (2011). On incentive compatible competitive selection protocols. Algorithmica, 61, 447–462.
5.
DugganJ.SchwartzT. (2000). Strategic manipulability without resoluteness or shared beliefs: Gibbard–Satterthwaite generalized. Social Choice and Welfare, 17, 85–93.
6.
FaliszewskiP. (2008). Manipulation of elections: Algorithms and infeasibility results. PhD thesis, University of Rochester, New York, NY.
