Multiple-task and multiple-agent models: Incentive contracts and an application to point pollution control

Two types of linear-quadratic principal-agent models will be considered: one in which a single agent has to perform several tasks and one in which several agents have to perform a certain task. For both models, we derive optimal contractual principal-agent relations. It turns out that under certain conditions (concerning risk-aversion and the correlation of the agents' outcome) the multiple-agent problem reduces to a multiple-task one-agent problem. Our results will be discussed within the framework of (multiple-) point pollution to which, in addition, also the results of the standard principal-agent model will be applied.