Stochastic mechanisms in settings without monetary transfers: regular case

We study relative performance of stochastic and deterministic mechanisms in a principal-agent model with hidden information and no monetary transfers. We present an example in which stochastic mechanisms perform strictly better than deterministic ones and can implement any outcome arbitrarily close to the first-best. Nevertheless, under the common assumption of quadratic payoffs and a certain regularity condition on the distribution of private information and the agent's bias, the optimal mechanism is deterministic. We provide an explicit characterization of this mechanism.