Opinion Control Competition in a Social Network

An SI₁ SI₂ S model represents the opinion dynamics for two opposing opinions over a social network. Two controllers with budget constraints, each representing one of the two opinions, wish to maximize a function of the number of nodes adopting their opinion at the end of a campaign that runs for a fixed duration. We determine the Nash control strategies for both the controllers and first prove a key structural result on these strategies that gives us insights on how campaigns should distribute their effort and ad spend. Next, via extensive simulation studies, we show that not being strategic may lead to a significant loss of effectiveness. We also observe that the relative values of the budgets of the two controllers are more significant than the absolute values of the budgets. Further, we study the allocation of budget across the duration of the campaign by the Nash strategies.