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Title: Winner-Take-All Tournaments

Author(s): Mikhail Drugov and Dmitry Ryvkin

Publication Date: May 2017

Keyword(s): dispersive order, entropy, failure rate, log-supermodularity, stochastic number of players, tournament, Tullock contest and unimodality

Programme Area(s): Industrial Organization

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.

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Bibliographic Reference

Drugov, M and Ryvkin, D. 2017. 'Winner-Take-All Tournaments'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=12067