DP12067 Winner-Take-All Tournaments

Author(s): Mikhail Drugov, Dmitry Ryvkin
Publication Date: May 2017
Keyword(s): dispersive order, entropy, failure rate, log-supermodularity, stochastic number of players, tournament, Tullock contest, unimodality
JEL(s): C72, D72, D82
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=12067

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.