Costly agreement-based transfers and targeting on networks with synergies

We consider agents organized in an undirected network of local complementarities. A principal with a limited budget offers costly bilateral contracts in order to increase the sum of agents' effort. We study excess-effort linear payment schemes, i.e. contracts rewarding effort in excess to the effort made in absence of principal. The analysis provides the following main insights. First, for all contracting costs, the optimal unit returns offered to every targeted agent are positive and generically heterogeneous. This heterogeneity is due to the presence of outsiders, who create asymmetric interaction between contracting agents. Second, when contracting costs are low, it is optimal to contract with everyone and optimal unit returns are identical for all agents. Third, when contracting costs are sufficiently high, it becomes optimal to target a subset of agents, and optimal targeting can lead to NP-hard problems. In particular, when the intensity of complementarities is sufficiently low, a correspondence is established between optimal targeting and the densest k subgraph problem. Overall, the optimal targeting problem involves a trade-off between centrality and budget spending-central agents are influential, but are also more budget-consuming. These considerations can lead the principal to not target central agents.