Locally robust contracts for moral hazard

We consider a moral hazard problem in which the principal has a slight uncertainty about how the agent’s actions translate into output. An incentive contract can be made robust against an $ϵ$ amount of uncertainty, at the cost of a loss to the principal on the order of $\sqrt{ϵ}$, by refunding a small fraction of profit to the agent. We show that as $ϵ$ goes to zero, this construction is essentially optimal, in the sense of minimizing the worst-case loss, among all modifications to the contract that do not depend on the details of the environment.