Multitask rank order tournaments

This work extends Lazear and Rosen's seminal paper to evaluate the performance of rank order tournaments when agents perform multiple tasks and the principal chooses, together with the prize spread, the weights assigned to each task in determining aggregate performance of each agent. All essential results of one-dimensional tournaments generalize to a multi-dimensional setting. However, the relative performance of tournaments and linear piece rates is shown to also depend on the covariance between measurement errors.