Social Science Job Candidate Seminar

I study a dynamic relationship in which a principal delegates experimentation to an agent. Experimentation is modeled as a two-armed bandit whose risky arm yields successes following a Poisson process. Its intensity, unknown to the players, is either high or low. The agent has private information, his type being his prior belief that the intensity is high. The agent values successes more than the principal and therefore prefers to experiment longer. I show how to reduce the analysis to a finite-dimensional problem. In the optimal contract, the principal starts with a calibrated prior belief and updates it as if the agent had no private information. The agent is free to experiment or not if this belief remains above a cutoff. He is required to stop once it reaches the cutoff. The cutoff binds for a positive measure of high enough types. Surprisingly, this delegation rule is time-consistent. I prove that the cutoff rule remains optimal and time-consistent for more general stochastic processes governing payoffs.