DP12368 Optimal Tournaments

Author(s): Mikhail Drugov, Dmitry Ryvkin
Publication Date: October 2017
Keyword(s): comparative statics, convex transform order, dispersive order, failure rate, optimal allocation of prizes, tournament, unimodality
JEL(s): C72, D72, D82
Programme Areas: Industrial Organization
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=12368

We study the optimal allocation of prizes and comparative statics of multi-prize rank-order tournaments. For a principal allocating a fixed budget, we show that the winner-take-all (WTA) prize schedule is optimal when the distribution of noise has an increasing failure rate (IFR). For noise distributions with unimodal failure rates the optimal prize allocation moves closer to WTA as the noise distribution becomes smaller in the convex transform order. We also identify a natural ordering of prize schedules by how closely they approximate the WTA schedule and show that for log-concave noise distributions the equilibrium effort is monotone in this order. The impact of noise intensity on equilibrium effort is captured by the dispersive order.