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A principal delegates decisions to a biased agent. Payoffs depend on a state that the principal cannot observe. Initially, the agent does not observe the state, but he can acquire information about it at a cost. We characterize the principal's optimal delegation set. This set features a cap on high decisions and a gap around the agent's ex ante favorite decision. It may even induce ex-post Pareto-dominated decisions. Under certain conditions on the cost of information acquisition, we show that the principal prefers delegating to an agent with a small bias than to an unbiased agent.
Ball et al. (Tue,) studied this question.