Working Paper: CEPR ID: DP14457
Authors: Mikhail Drugov; Dmitry Ryvkin
Abstract: It is commonly understood that making a tournament ranking process more noisy leads to a reduction in effort exerted by players in the tournament. But what exactly does it mean to have ``more noise?'' We address this question and show that the level of risk, as measured by the variance or the second-order stochastic dominance order, is not the answer, in general. For rank-order tournaments with arbitrary prizes, equilibrium effort decreases as noise becomes more dispersed, in the sense of the dispersive order. For winner-take-all tournaments, we identify a weaker version of the dispersive order we call quantile stochastic dominance, as well as other orders and entropy measures linking equilibrium effort and noise.
Keywords: tournament; noise; dispersive order; quantile stochastic dominance; entropy
JEL Codes: C72; D72; D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| increasing noise in tournament ranking processes (C73) | decrease in equilibrium effort exerted by players (D59) |
| more dispersed noise distribution x (C46) | higher equilibrium effort than noise distribution y (D59) |
| dispersive order (C69) | ranking of noise distributions in terms of equilibrium efforts (C46) |
| entropy (D89) | determining equilibrium effort (C62) |
| probability densities of differences between shocks (C46) | influence on marginal incentives in tournaments (C72) |