Working Paper: CEPR ID: DP12067
Authors: Mikhail Drugov; Dmitry Ryvkin
Abstract: This paper provides new general results for winner-take-all rank-order tournaments with additive and multiplicative noise. We show that the comparative statics of the individual equilibrium effort with respect to the number of players follow the shape of the density the noise distribution. For aggregate effort, a similar relation holds for the failure (hazard) rate of the noise distribution. The equilibrium effort decreases as noise becomes more dispersed, in the sense of the dispersive order or appropriately defined entropy. These results are then extended to the case of a stochastic number of players, and new results on the effects of population uncertainty are obtained. All relevant results for the Tullock contest follow as a special case.
Keywords: Tournament; Stochastic Number of Players; Unimodality; Log-Supermodularity; Failure Rate; Entropy; Dispersive Order
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 |
|---|---|
| noise dispersion (Y40) | equilibrium effort (D50) |
| number of players (C72) | individual probability of winning (C25) |
| number of players (C72) | equilibrium effort (D50) |
| unimodal noise distribution (C46) | equilibrium effort (D50) |
| distribution of noise characteristics (C46) | equilibrium effort (D50) |