Optimal Multi-Agent Performance Measures for Team Contracts

We present a continuous-time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sufficient statistic, and the other a non-sufficient statistic. As a consequence, the optimal aggregate performance measure in general is not a sufficient statistic, except when the principal is risk neutral. We further discuss agents' optimal effort choices using a "quadratic-cost" example, which also strikingly suggests that team contracts sometimes provide lower-powered effort incentives than individually separate contracts do.