Sequential tasks and moral hazard

A principal owns a two-stage project consisting of two tasks with a finish-to-start dependency where there exists an outcome externality between these tasks. A success in the first task may affect the probability of success of the second task in a positive or negative way, which refers to synergistic and conflicting tasks, respectively. We analyze the optimal incentive schemes where both the number of agents and the order of the tasks are endogenous. We find that, regardless of the optimal set of agents, when both tasks are synergistic, the task with the greater impact is delegated first, while when tasks are conflicting, the one with the lower impact is scheduled first. When one task is synergistic and the other one is conflicting, the principal prefers the synergistic task to be completed first. When the task order is endogenously determined, the principal prefers to employ two identical agents for two different tasks when the tasks are synergistic and a single agent for two tasks when both tasks are conflicting. Since the task allocation is endogenous, we let one task to be synergistic and the other one to be conflicting, in which case it is optimal for the principal to hire two different agents. These results are robust to a possible wage payment after the completion of each task.