Winner-Take-All Tournaments

67 Pages Posted: 5 Jun 2017

See all articles by Mikhail Drugov

Mikhail Drugov

Centre for Economic Policy Research (CEPR); New Economic School (NES)

Dmitry Ryvkin

Florida State University

Date Written: May 2017


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: dispersive order, entropy, failure rate, log-supermodularity, stochastic number of players, tournament, Tullock contest, unimodality

JEL Classification: C72, D72, D82

Suggested Citation

Drugov, Mikhail and Ryvkin, Dmitry, Winner-Take-All Tournaments (May 2017). CEPR Discussion Paper No. DP12067, Available at SSRN:

Mikhail Drugov (Contact Author)

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026

Dmitry Ryvkin

Florida State University ( email )

Tallahassee, FL 30306-2180
United States

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