Leveraging Network Topology in a Two-way Competition for Influence in the Friedkin-Johnsen Model

In this paper, we consider two stubborn agents who compete for `influence' over a strongly connected group of agents. This framework represents real-world contests, such as competition among firms, two-party elections, and sports rivalries, among others. Considering stubbornness of agents to be an immutable property, we utilise the network topology alone to increase the influence of a preferred stubborn agent. We demonstrate this on a special class of strongly connected networks by identifying the supporters of each of the stubborn agents in such networks. Thereafter, we present sufficient conditions under which a network perturbation always increases the influence of the preferred stubborn agent. A key advantage of the proposed topology-based conditions is that they hold independent of the edge weights in the network. Most importantly, we assert that there exists a sequence of perturbations that can make the lesser influential stubborn agent more influential. Finally, we demonstrate our results over the Sampson's Monastery dataset.