Noisy Observation in Adverse Selection Models
研究委托代理问题中代理人行为只能被噪声观测时的合同设计，分析线性与二次奖励计划在何种条件下能实现无噪声时的最优机制，并给出几何直觉。
We consider a principal-agent contracting problem under incomplete information where some of the agent's actions are imperfectly observable. Contracts take the form of reward schedules based on the noisy observation of the agent's action. We first review situations where the principal can reach the same utility as in the absence of noise. Then we focus on the use of linear reward schedules, which allow universal implementation, i.e. implementation of a given mechanism for any unbiased noise of observation, and on quadratic reward schedules, which only require the knowledge of the variance of the noise. We exhibit sufficient conditions under which linear reward schedules implement a given mechanism. Finally, we characterize necessary conditions for a mechanism to be implementable under noisy observation by a linear schedule, and by quadratic schedules. We give the geometric intuition behind all results.