  Networked public goods games model scenarios in which self-interested agents
decide whether or how much to invest in an action that benefits not only
themselves, but also their network neighbors. Examples include vaccination,
security investment, and crime reporting. While every agent's utility is
increasing in their neighbors' joint investment, the specific form can vary
widely depending on the scenario. A principal, such as a policymaker, may wish
to induce large investment from the agents. Besides direct incentives, an
important lever here is the network structure itself: by adding and removing
edges, for example, through community meetings, the principal can change the
nature of the utility functions, resulting in different, and perhaps socially
preferable, equilibrium outcomes. We initiate an algorithmic study of targeted
network modifications with the goal of inducing equilibria of a particular
form. We study this question for a variety of equilibrium forms (induce all
agents to invest, at least a given set $S$, exactly a given set $S$, at least
$k$ agents), and for a variety of utility functions. While we show that the
problem is NP-complete for a number of these scenarios, we exhibit a broad
array of scenarios in which the problem can be solved in polynomial time by
non-trivial reductions to (minimum-cost) matching problems.
