Abstract:
We study the problem of optimal contract design in an environment with an uninformed decision maker and two perfectly informed experts. The experts can be paid for their advice but have limited liability, i.e., the payments cannot be negative. In order to characterize optimal contracts for the decision maker, we prove a "constant-threat principle" that states that one can restrict attention to contracts in which the action implemented in case of a disagreement among the experts is independent of their reports. This result tremendously reduces the complexity of the contract design problem. We describe optimal contracts and, in particular, provide some necessary and sufficient conditions under which these contracts implement the first best outcome at zero cost. Furthermore, we show that in a class of standard environments the optimal contract employs no payments to the experts even if the first best outcome is not implemented. We compare optimal contracts in our model with optimal contracts in environments with one expert and observe that adding a second expert is always valuable; this is so even if the bias of the expert is arbitrary large.