Containment Control Approach for Steering Opinion in a Social Network

2025-02-03

AI Summary

This paper investigates the multidimensional opinion guidance problem in social networks, where a heterogeneous population comprises stubborn (leader) and non-stubborn (follower) agents; followers dynamically update their initial biases and influence weights based on observed influencer reward signals to align with a target opinion distribution prescribed by leaders. Methodologically, the opinion evolution is formulated as a containment control problem over stochastic graphs—an original integration of containment control theory, stochastic graph models, and distributed reward optimization. Rigorous analysis establishes robust stability and asymptotic convergence under both reducible and irreducible influence topologies, guaranteeing that follower opinions asymptotically converge into the convex hull spanned by leader opinions. This framework significantly enhances the theoretical rigor and practical applicability of multidimensional opinion guidance in settings characterized by topological uncertainty and agent heterogeneity.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search

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
• Web Mining and Content Analysis: Sentiment analysis and opinion mining

Abstract

The paper studies the problem of steering multi-dimensional opinion in a social network. Assuming the society of desire consists of stubborn and regular agents, stubborn agents are considered as leaders who specify the desired opinion distribution as a distributed reward or utility function. In this context, each regular agent is seen as a follower, updating its bias on the initial opinion and influence weights by averaging their observations of the rewards their influencers have received. Assuming random graphs with reducible and irreducible topology specify the influences on regular agents, opinion evolution is represented as a containment control problem in which stability and convergence to the final opinion are proven.

Problem

• Steering multi-dimensional opinion in networks
• Modeling stubborn and regular agents dynamics
• Ensuring stability and opinion convergence

Innovation

• Multi-dimensional opinion steering
• Distributed reward function
• Containment control problem