Tournaments As Optimal Contracts

The author considers a standard multi-agent moral hazard problem with an added assumption that puts an upper bound on wages. The author shows that when the distribution of the aggregate shock to output is the diffused prior, a compensation scheme based on the demeaned vector of outputs is optimal. The author derives conditions on the distributions of the noise terms under which, in the 2-agent case, the optimal compensation scheme is a tournament or a tournament with a tie. Aside from providing a theoretical explanation for the existence of tournaments, the analysis suggests circumstances in which tournaments are more likely to be observed.