Uniqueness of Solutions to Principal-Agent Problems

For a broad class of principal-agent problems, and for "almost all" specifications of the probability distribution over types, the principal has an essentially unique optimal mechanism: any two optimal mechanisms will agree, for each type of the agent, in the payoff they yield to both the principal and the agent. The model allows for arbitrary risk preferences, the possibility of randomization, and both a hidden type and action. The substantive assumptions are that the set of types is finite, and a certain separability of the utility of the agent.