Learning from Failures: Optimal Contract for Experimentation and Production

Before embarking on a project, a principal must often rely on an agent to learn about its profitability. We model this learning as a two-armed bandit problem and highlight the interaction between learning (experimentation) and production. We derive the optimal contract for both experimentation and production when the agent has private information about his efficiency in experimentation. This private information in the experimentation stage generates asymmetric information in the production stage even though there was no disagreement about the profitability of the project at the outset. The degree of asymmetric information is endogenously determined by the length of the experimentation stage. An optimal contract uses the length of experimentation, the production scale, and the timing of payments to screen the agents. Due to the presence of an optimal production decision after experimentation, we find over-experimentation to be optimal. The asymmetric information generated during experimentation makes over-production optimal. An efficient type is rewarded early since he is more likely to succeed in experimenting, while an inefficient type is rewarded at the very end of the experimentation stage. This result is robust to the introduction of ex post moral hazard.