We consider a bandit problem faced by a team of two heterogeneous players. The team is hierarchical in that one (the principal) retains the exclusive right to terminate the project while the other (the agent) focuses strictly on implementing the project assigned to him. As a key departure, we assume that the principal may be privately informed about the project quality. In contrast to the existing literature, the belief in our model is generally non-monotonic: while each failure makes the agent less confident in the project, the uninformed principal drops out gradually over time, which partially restores his confidence. We derive explicit solutions for the agent's effort and the principal's exit decisions, which allow us to obtain a full characterization of the equilibrium. We also discuss the role of effort monitoring in this context and suggest a new rationale for delegation.
bandit problems experimentation hierarchy role specialization war of attrition delegation