Welfare and Distributional Effects of Joint Intervention in Networks

TL;DR

This paper analyzes how a planner can optimally influence both agents' utilities and network links to maximize welfare, revealing structural patterns and trade-offs between efficiency and inequality.

Contribution

It introduces a model of joint intervention in networks, characterizing optimal strategies and welfare effects, and compares joint versus single interventions.

Findings

Optimal link changes are proportional to eigen-centralities under moderate budgets.

Large budgets lead to complete or bipartite network structures depending on strategic interactions.

Joint interventions improve welfare but may increase inequality.

Abstract

We study the optimal joint intervention of a planner who can influence both the standalone marginal utilities of agents in a network and the weights of the links connecting them. The welfare-maximizing intervention displays two key features. First, when the planner's budget is moderate (yielding interior solutions), the optimal change in link weight between any pair of agents is proportional to the product of their eigen-centralities. Second, when the budget is sufficiently large, the optimal network converges to a simple structure: a complete network under strategic complements, or a complete balanced bipartite network under strategic substitutes. We show that welfare effects are governed by the principal eigenvalue of the network, while distributional outcomes are driven by the dispersion of the corresponding eigen-centralities. Comparing joint interventions to single interventions targeting only standalone marginal utilities, we find that joint interventions consistently generate higher aggregate welfare, but may also increase inequality, revealing a potential trade-off between efficiency and equity.