Moral hazard on networks

In a multi-agent contracting setting, agents' performances are related due to both correlating noise and effort spillover. We study the optimal linear contract in which the agents are risk averse. Putting compensation weights on peers' performances helps to filter out common noise, which relaxes the participation constraint (hedge effect). However, it may also discourage the incentive to exert effort due to effort spillover, which therefore tightens the incentive compatibility constraint (incentive effect). We show that optimal compensation sensitivity is determined by the dot product between pure hedge vector and spillover vector. Besides, we propose an index called informativeness along the spillover direction to capture the balance between hedge and incentive effects. As a result, both the induced effort and generated profit in equilibrium are positively related with this index. Finally, we demonstrate the disparity between spillover depth (measuring the strength of spillover effect) and spillover width (summarizing the density of spillover structure)