The Effect of Network Topology on the Equilibria of Influence-Opinion Games

Online social networks exert a powerful influence on public opinion. Adversaries weaponize these networks to manipulate discourse, underscoring the need for more resilient social networks. To this end, we investigate the impact of network connectivity on Stackelberg equilibria in a two-player game to shape public opinion. We model opinion evolution as a repeated competitive influence-propagation process. Players iteratively inject \textit{messages} that diffuse until reaching a steady state, modeling the dispersion of two competing messages. Opinions then update according to the discounted sum of exposure to the messages. This bi-level model captures viral-media correlation effects omitted by standard opinion-dynamics models. To solve the resulting high-dimensional game, we propose a scalable, iterative algorithm based on linear-quadratic regulators that approximates local feedback Stackelberg strategies for players with limited cognition. We analyze how the network topology shapes equilibrium outcomes through experiments on synthetic networks and real Facebook data. Our results identify structural characteristics that improve a network's resilience to adversarial influence, guiding the design of more resilient social networks.