Dynamic Contracts for a Class of Multi - Agent R & D Models ∗ ( Job Market Paper Two )

Most R&D projects are executed by employing teams of researchers and in distinct phases. These two features distinguish the agency problem that a firm faces with respect to its inhouse R&D unit from traditional principal-agent problems. This paper analyzes this agency problem by studying a continuous-time multi-agent incentive problem in which a principal hires two risk-averse agents to perform a multi-stage R&D project. The completion of each stage is modeled by a Poisson type process, where the probability of success is jointly determined by the actions of both agents. We use recursive methods to characterize the optimal dynamic contract in this set-up. Our main result provides a new insight into the optimal incentive regime for multi-agent moral-hazard problems. In particular, we show explicitly the way in which the optimal incentive regime is a function of how agents’ efforts interact with one another: relativeperformance evaluation is used when their efforts are substitutes whereas joint-performance evaluation is used when their efforts are complements.