Optimal delegation with multi-dimensional decisions

This paper investigates optimal mechanisms in a principal–agent framework with a two-dimensional decision space, quadratic payoffs and no monetary transfers. If the conflicts of interest between the principal and the agent are different on each dimension, then delegation is always strictly valuable. The principal can better extract information from the agent by using the spread between the two decisions as a costly screening device. Delegation sets no longer trade off pooling intervals and intervals of full discretion but instead take more complex shapes. We use advanced results from the calculus of variations to ensure existence of a solution and derive sufficient and necessary conditions for optimality. The optimal mechanism is continuous and deterministic. The agentʼs informational rent, the average decision and its spread are strictly monotonic in the agentʼs type. The comparison of the optimal mechanism with standard one-dimensional mechanisms shows how cooperation between different principals controlling various dimensions of the agentʼs activities facilitates information revelation.