Optimal Prizes in Tournaments Under Nonseparable Preferences
We study rank-order tournaments with risk-averse agents whose utility over money and effort (or leisure) may be nonseparable. We characterize optimal prize schedules when the principal allocates a fixed budget and show how they are determined by the interplay between the properties of noise and the utility function. In particular, the distribution of noise alone determines whether the optimal prize schedule has flat regions where prizes are equal, while the total number of positive prizes depends on both the noise distribution and utility. For unimodal noise distributions, the optimal number of positive prizes is restricted regardless of utility under mild assumptions. Also, while the common wisdom suggests---and it holds in the separable case---that risk aversion pushes optimal prize allocations in the direction of prize sharing, this is no longer true, in general, when the marginal utility of money depends on effort.