Contracting a crowd of heterogeneous agents

We study a principal-agent model involving a large population of heterogeneously interacting agents. By extending the existing methods, we find the optimal contracts assuming a continuum of agents, and show that, when the number of agents is sufficiently large, the optimal contracts for the problem with a continuum of agents are near-optimal for the finite agents problem. We make comparative statistics and provide numerical simulations to analyze how the agents' connectivity affects the principal's value, the effort of the agents, and the optimal contracts.