DP14457 How noise affects effort in tournaments

Author(s):	Mikhail Drugov, Dmitry Ryvkin
Publication Date:	February 2020
Keyword(s):	dispersive order, entropy, noise, quantile stochastic dominance, tournament
JEL(s):	C72, D72, D82
Programme Areas:	Industrial Organization
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=14457

It is commonly understood that making a tournament ranking process more noisy leads to a reduction in effort exerted by players in the tournament. But what exactly does it mean to have "more noise?'' We address this question and show that the level of risk, as measured by the variance or the second-order stochastic dominance order, is not the answer, in general. For rank-order tournaments with arbitrary prizes, equilibrium effort decreases as noise becomes more dispersed, in the sense of the dispersive order. For winner-take-all tournaments, we identify a weaker version of the dispersive order we call quantile stochastic dominance, as well as other orders and entropy measures linking equilibrium effort and noise.