Coordination Games on Multiplex Networks: Consensus, Convergence, and Stability of Opinion Dynamics

2026-03-08

AI Summary

This study investigates consensus formation, convergence, and stability in opinion dynamics over multilayer social networks. Opinion updates are modeled as synchronous coordination games, and two interlayer coupling mechanisms—fusion and switching—are proposed to capture how individuals evolve their opinions by minimizing local costs to align with neighbors. Leveraging stochastic walks and spectral methods, the theoretical analysis establishes sufficient conditions for consensus, characterizes convergence rates, and evaluates robustness under network perturbations. The work reveals that multilayer interactions can either induce or accelerate global consensus—even when individual layers fail to reach agreement—but may also disrupt otherwise coherent consensus due to interlayer coupling. Numerical experiments confirm the critical influence of layer weights and switching periods on consensus outcomes.

Technology Category

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

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper studies opinion dynamics in multilayer social networks. Extending a single-layer model, we formulate opinion updates as a synchronous coordination game in which agents minimize a local cost to stay close to their neighbors'opinions. We propose two coupling mechanisms: (i) a merged model that aggregates layers through weighted influences, and (ii) a switching model that periodically alternates across layers. Using random-walk and spectral analysis, we derive sufficient conditions for consensus, characterize convergence rates, and analyze stability under network perturbations. We show that multilayer interactions can induce or accelerate global consensus even when no single layer achieves it alone, and conversely, that individually coordinated layers may lose consensus once interconnected. Numerical experiments validate the theory and highlight the impact of layer weights and switching periods. These results clarify how cross-network interactions shape coordination and information diffusion across interconnected systems.

Problem

• Coordination Games
• Multiplex Networks
• Opinion Dynamics
• Consensus
• Multilayer Networks

Innovation

• multiplex networks
• coordination games
• opinion dynamics
• consensus
• spectral analysis