  In this paper we consider an extension of the well-known Influence
Maximization Problem in a social network which deals with finding a set of k
nodes to initiate a diffusion process so that the total number of influenced
nodes at the end of the process is maximized. The extension focuses on a
competitive variant where two decision makers are involved. The first one, the
leader, tries to maximize the total influence spread by selecting the most
influential nodes and the second one, the follower, tries to minimize it by
deactivating some of these nodes. The formulated bilevel model is solved by
complete enumeration for small-sized instances and by a matheuristic for
large-sized instances. In both cases, the lower level problem, which is a
stochastic optimization problem, is approximated via the Sample Average
Approximation method.
