  Social influence is largely recognized as a key factor in opinion formation
processes. Recently, the role of external forces in inducing opinion
displacement and polarization in social networks has attracted significant
attention. This is in particular motivated by the necessity to understand and
possibly prevent interference phenomena during political campaigns and
elections. In this paper, we formulate and solve a targeted intervention
problem for opinion displacement minimization on a social network.
Specifically, we consider a min-max problem whereby a social planner (the
defender) aims at selecting the optimal network intervention within her given
budget constraint in order to minimize the opinion displacement in the system
that an adversary (the attacker) is instead trying to maximize. Our results
show that the optimal intervention of the defender has two regimes. For large
enough budget, the optimal intervention of the social planner acts on all nodes
proportionally to a new notion of network centrality. For lower budget values,
such optimal intervention has a more delicate structure and is rather
concentrated on a few target individuals.
