Approximate Optimality of Linear Contracts Under Uncertainty

We consider a hidden-action principal-agent model, in which actions require different amounts of effort, and the agent privately knows his ability that determines his cost of effort. We show that linear contracts admit approximation guarantees that improve with a natural metric that captures the degree of uncertainty in the contracting setting. We thus show that linear contracts are near-optimal whenever there is enough uncertainty. In contrast, other simple contract formats such as debt contracts may suffer from a loss linear in the number of possible actions, even when there is sufficient uncertainty.