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

2025-06-27

AI Summary

This study investigates how network topology influences equilibrium outcomes in influence-opinion games, aiming to uncover structural mechanisms underlying social networks’ resilience against opinion manipulation. Method: We propose a two-layer dynamic game model integrating competitive information diffusion with opinion evolution dynamics. To capture users’ bounded attention, we introduce a novel discounted exposure accumulation update mechanism. Furthermore, we design a scalable feedback Stackelberg algorithm based on linear-quadratic regulation to approximate optimal intervention strategies under cognitive constraints. Results: Experiments on synthetic networks and real-world Facebook data identify three critical topological features governing network resilience: node centrality distribution, local clustering coefficient, and inter-community edge density. Our findings provide both theoretical foundations and computationally tractable design principles for constructing robust, manipulation-resistant social networks.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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 extit{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.

Problem

• Impact of network topology on opinion-game equilibria
• Modeling adversarial influence in social networks
• Designing resilient networks against opinion manipulation

Innovation

• Model opinion evolution as competitive influence-propagation process
• Propose scalable iterative algorithm using linear-quadratic regulators
• Analyze network topology impact on equilibrium outcomes