Optimal contracts with random monitoring

We study an optimal contract problem under moral hazard in a principal-agent framework where contracts are implemented through random monitoring. This is a monitoring instrument that reveals the precise action taken by the agent with some nondegenerate probability, and otherwise reveals no information. The agent's cost of performing the action depends on a random state of nature. This state is private information to the agent, but can be non-verifiably communicated, allowing the contract to specify wages as a function of the agent's message. We show that the optimal contract partitions the set of types in three regions. The most efficient types exert effort and receive a reward when monitored. Moderately efficient types exert effort but are paid the same wage with monitoring as without. The least efficient types do not exert effort. More intense monitoring increases the value of a contract when the agent is risk averse.