How to Win Nodes and Influence Networks: A Multidimensional Approach to Opinion Dynamics and Influence Games

Abstract

In a period where socialization is hyper-reliant on digital platforms, permitting information to spread instantaneously, understanding strategies for optimal influence is vital. This paper develops a multidimensional, threshold-based opinion dynamics model extending the work from DeGroot and Friedkin-Johnsen. Our model incorporates intertopic dependencies and external influence to model competitive diffusion over networks. We introduce a novel opinion update rule that incorporates local (neighbor) and global (external players) impact on opinion shifts. Through coupling linear threshold dynamics with traditional opinion models (FJ) and introducing intricacies of topic dependencies and multidimensional opinions, our model emulates realistic evolution of opinion and behavior. By simulating over synthetic and real-world data from the General Social Survey (GSS), we assess strategies of one and two-player models where influence is maximized. Results reveal that optimal strategies depend critically on initial opinion distribution, network topology, and the interdependence of topics. In particular, optimal strategies surface that leverage indirect influence by exploiting cross-topic relationships, and in the presence of competition, second movers gain a strategic edge. This work provides practical insight for designing self-regulating environments in polarized societies by strategically disseminating information. The implications of this research range from political campaigns, public health messaging, and ethical information diffusion.