Relative performance evaluation in a multi-plant firm

We analyze optimal compensation schedules for the directors of two plants belonging to the same owner and producing the same good but serving geographically differentiated markets. Since the outcome of each director depends on his own effort and on a random variable representing market conditions, the problem takes the form of a principal multi-agent model. We first provide appropriate extensions of the MLR and CDF conditions that ensure the validity of the first-order approach in the single agent case. Then, we show that affiliation of the random variables is a necessary and sufficient condition for the compensation of one director to negatively and monotonically depend on the performance of the other.