Welfare and Distributional Effects of Joint Intervention in Networks

We study a planner's optimal interventions in both the standalone marginal utilities of players on a network and weights on the links that connect players. The welfare-maximizing joint intervention exhibits the following properties: (a) when the planner's budget is moderate (so that optimal interventions are interior), the change in weight on any link connecting a pair of players is proportional to the product of eigen-centralities of the pair; (b) when the budget is sufficiently large, the optimal network takes a simple form: It is either a complete network under strategic complements or a complete balanced bipartite network under strategic substitutes. We show that the welfare effect of joint intervention is shaped by the principal eigenvalue, while the distributional effect is captured by the dispersion of the corresponding eigenvalues, i.e., the eigen-centralities. Comparing joint intervention in our setting with single intervention solely on the standalone marginal utilities, as studied by Galeotti et al. (2020), we find that joint intervention always yields a higher aggregate welfare, but may lead to greater inequality, which highlights a possible trade-off between the welfare and distributional impacts of joint intervention.