Combinatorial agency

We study a combinatorial variant of the classical principal-agent model. In our setting a principal wishes to incentivize a team of strategic agents to exert costly effort on his behalf. Agents' actions are hidden and the principal observes only the outcome of the team, which depends stochastically on the complex combinations of the efforts by the agents. The principal seeks the mechanism that maximizes the principal's net revenue given an equilibrium behavior of the agents. We investigate the structure of the optimal mechanism for various production technologies as the principal's value from the project varies. In doing so we quantify the gap between the first-best and second-best solutions. Our results highlight the qualitative and quantitative differences between production technologies that exhibit complementarities and substitutabilities between the agents' actions. In comparing the first best with the second best we highlight the role of effort monitoring by the principal. As we shall see, the benefit from monitoring crucially depends on the underlying technology, with the two polar cases being perfect substitution and perfect complementarity.