Team Incentives with Imperfect Mutual Inference

I study the optimal team incentive when the agents can coordinate private actions through repeated interaction with imperfect public monitoring. The agents are able to imperfectly infer each other's private actions via the stochastically correlated measurements. Correlation of measurement noise, besides its risk sharing role in the conventional multiple-agent moral hazard problem, is crucial to the accuracy of each agent's inference. The principal's choice of performance pay to provide incentive via inducing competition or coordination among the agents thus exhibits the trade-off between risk sharing and mutual inference between the agents. I characterize the optimal form of performance pay with respect to the correlation of measurement noise. Whether the conventional theoretical prediction holds depends on how the agents form the mutual inference, based on an exogenous standard or formed endogenously