Stochastic mechanisms in settings without monetary transfers: The regular case

Abstract

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.

Optimal sequential delegation

“…It is well-known that in this case, the optimal delegation set is an interval with upper endpoint β 0 p . 19 Note that by assumption (1), ω p < β 0 p . We summarize this result in the following lemma.…”

“…Instead of providing incentives for information acquisition, in our setup offering only extreme options provides incentives for the agent to reveal information about his ex ante expertise. Our paper draws heavily on the insights in Kováč and Mylovanov (2009) who provide a handy and intuitive representation of the principal's expected utility as a weighted average of the agent's utility. In particular, we exploit this representation to derive the optimal static delegation set in our setup.…”

“…In particular, we exploit this representation to derive the optimal static delegation set in our setup. This is not trivial since, for some parameters, our setup violates the conditions for which Alonso and Matouscheck (2008) or Kováč and Mylovanov (2009) characterize the solution to the static delegation problem. 2 Secondly, our paper is related to the literature on sequential screening in the spirit of Courty and Li (2000) who study a dynamic price discrimination problem where the agent, while knowing a private signal at the time of contracting, learns his actual willingness to pay at the time of consumption only over time.…”

“…It is useful to relate our results on optimal static delegation to the literature. The static problem has, in some generality, been studied by Alonso and Matouscheck (2008) and by Kováč and Mylovanov (2009). In particular, Kováč and Mylovanov (2009) show that the solution is interval delegation if the density associated with the distribution of the state is absolutely continuous, and a "regularity" condition holds.…”

“…The static problem has, in some generality, been studied by Alonso and Matouscheck (2008) and by Kováč and Mylovanov (2009). In particular, Kováč and Mylovanov (2009) show that the solution is interval delegation if the density associated with the distribution of the state is absolutely continuous, and a "regularity" condition holds. However, we cannot directly apply Kováč and Mylovanov (2009)'s result, because in our case, f is not absolutely continuous, as it has jumps at the points ω = ω and ω =ω ; thus, f is only piece-wise absolutely continuous.…”