Optimal Delegation Under Unknown Bias: The Role of Concavity
A principal is uncertain of an agent's preferences and cannot provide monetary transfers. The principal, however, does control the discretion granted to the agent. In this paper, we provide a simple characterization of when it is optimal for the principal to screen by offering different terms of discretion to the agent. When the principal's utility is sufficiently concave, it is optimal for the principal to pool and to offer all agents the same discretion. Thus, for any number of agents and any distribution over agent preferences, the optimal contract is simple: the principal sets a cap and forbids actions above this cap (interval delegation). For less concave preferences, it is optimal for the principal to screen. The principal benefits by providing agents a choice between interval delegation and gap delegation, which allows for more extreme actions but prohibits intermediate actions. Moreover, we provide new intuition for the optimality of interval delegation when the principal knows the agent's preferences: the payoff distributions generated by sets containing gaps are mean-preserving spreads of those generated by intervals.