Continuous Influence Maximisation for the Voter Dynamics: Is Targeting High-Degree Nodes a Good Strategy?

In this paper, we relate influence maximisation (IM) for the voting dynamics to models of network control in which external controllers interact with the intrinsic dynamics of opinion spread. In contrast to previous literature, which has mostly explored the discrete setting, our focus is on continuous allocations of control. We develop an algorithm to numerically solve our IM problem via gradient ascent. We explore optimal allocations for leader-follower type networks for different budget scenarios and observe that optimal allocations do not systematically target hub nodes, as it has been found in previous literature. Conversely, strategies are strongly opponent-depend, avoiding nodes targeted by the opponent if the opponent has a larger budget, while shadowing the opponent's allocation otherwise, i.e. targeting the same nodes as them.