Targeting Interacting Agents

We introduce a novel framework to study targeted policy interventions. Agents: 1) differ both in their likelihood of and loss from interaction, 2) exert negative externalities through interaction, and 3) can exert costly effort to isolate. Additionally, a planner can select a subset of agents to isolate from interaction at zero cost. Our main result is a full characterization of optimal policies when costly isolation is either voluntary or mandatory. When voluntary, optimal policy is non-monotone -- agents with intermediate vulnerability are selected more. Moreover, we uncover a novel form of risk compensation -- voluntary behavior implies that selection is redirected toward the vulnerable away from the interactive, to maintain incentives for self-isolation. We extend our insights to a setting with positive externalities, and apply our results to applications including vaccine allocation, platform design, and information aggregation.