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Optimal tournaments

Mikhail Drugov () and Dmitry Ryvkin ()

No wp2017_05_01, Working Papers from Department of Economics, Florida State University

Abstract: We study the optimal allocation of prizes, comparative statics and architecture 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 increasing failure rate (IFR). For noise distributions with unimodal failure rates the optimal prize allocation moves closer to WTA as the 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. Comparing one-stage tournaments with parallel tournaments where players are split into subgroups competing for separate prizes, we show that the former architecture always dominates for IFR noise distributions. However, when comparing one-stage tournaments to a two-stage architecture where first-stage winners from parallel subgroups compete in the second-stage tournament, we show that either of the two architectures can be optimal depending on the details of the distribution of noise, including noise dispersion.

Keywords: tournament; optimal allocation of prizes; unimodality; failure rate; comparative statics; architecture; dispersive order; convex transform order (search for similar items in EconPapers)
JEL-codes: C72 D72 D82 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-hrm and nep-mic
Date: 2017-05
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ftp://econpapers.fsu.edu/RePEc/fsu/wpaper/wp2017_05_01.pdf First version, 2017-05 (application/pdf)

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