  We study games in which a network mediates strategic spillovers and
externalities among the players. How does a planner optimally target
interventions that change individuals' private returns to investment? We
analyze this question by decomposing any intervention into orthogonal principal
components, which are determined by the network and are ordered according to
their associated eigenvalues. There is a close connection between the nature of
spillovers and the representation of various principal components in the
optimal intervention. In games of strategic complements (substitutes),
interventions place more weight on the top (bottom) principal components, which
reflect more global (local) network structure. For large budgets, optimal
interventions are simple -- they involve a single principal component.
