Dynamic Inspection and the Value of Information

This paper analyses a dynamic inspection game between a principal and agent where the agent has private information about his binary type. The principal strictly prefers employing the high type to his outside option, and the outside option to the low type. Every period, the agent can either exert effort or shirk, and the principal can monitor the agent's actions at a cost. The high type never shirks, while low types find effort costly. Monitoring provides a tool for learning about the agent's type. I show that the game generically has a unique equilibrium akin to a war of attrition between the principal and the low type. My main result is that monitoring provides valuable information for the principal if and only if he is sufficiently pessimistic about the agent's type. The probability of monitoring decreases as the agent's reputation grows. Eventually, either the low type is caught and fired, or the principal trusts the agent enough that monitoring ends forever