  We study the problem of optimally investing in nodes of a social network in a
competitive setting, wherein two camps aim to drive the average opinion of the
population in their own favor. Using a well-established model of opinion
dynamics, we formulate the problem as a zero-sum game with its players being
the two camps. We derive optimal investment strategies for both camps, and show
that a random investment strategy is optimal when the underlying network
follows a popular class of weight distributions. We study a broad framework,
where we consider various well-motivated settings of the problem, namely, when
the influence of a camp on a node is a concave function of its investment on
that node, when a camp aims at maximizing competitor's investment or deviation
from its desired investment, and when one of the camps has uncertain
information about the values of the model parameters. We also study a
Stackelberg variant of this game under common coupled constraints on the
combined investments by the camps and derive their equilibrium strategies, and
hence quantify the first-mover advantage. For a quantitative and illustrative
study, we conduct simulations on real-world datasets and provide results and
insights.
