Targeting Interventions in Networks
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Individuals interact strategically with their network neighbors, as in effort investment with spillovers among peers, or production decisions among firms connected by a supply chain. A planner can shape their incentives in pursuit of some goal -- for instance, maximizing utilitarian welfare or minimizing the volatility of aggregate activity. We offer an approach to solving such intervention problems that exploits the singular value decomposition of network interaction matrices. The approach works by (i) describing the game in new coordinates given by the singular value decomposition of the network on which the game is played; and (ii) using that to deduce which components, and hence which individuals, a given type of intervention will focus on. Across a variety of intervention problems, simple orderings of the principal components characterize the planner's priorities.
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