Game Theory Based Community-Aware Opinion Dynamics

TL;DR

The paper presents GCAOFP, a two-stage framework for co-evolving communities and opinions in networks by combining a welfare-maximizing non-cooperative community dynamics game with a bounded-confidence opinion update. It provides theoretical convergence guarantees to a finite-time equilibrium where both opinions and community partitions stabilize, and demonstrates that convergence occurs locally within communities. Empirical results on real-world networks show improved social welfare and higher-quality community partitions compared to baselines, with favorable scalability and clear parameter effects on convergence and partitioning. The approach offers a principled mechanism to integrate network structure and agent opinions, with potential implications for tasks such as link prediction and more realistic modeling of social dynamics.

Abstract

Examining the mechanisms underlying the formation and evolution of opinions within real-world social systems, which consist of numerous individuals, can provide valuable insights for effective social functioning and informed business decision making. The focus of our study is on the dynamics of opinions inside a networked multi-agent system. We provide a novel approach called the Game Theory Based Community-Aware Opinion Formation Process (GCAOFP) to accurately represent the co-evolutionary dynamics of communities and opinions in real-world social systems. The GCAOFP algorithm comprises two distinct steps in each iteration. 1) The Community Dynamics Process conceptualizes the process of community formation as a non-cooperative game involving a finite number of agents. Each individual agent aims to maximize their own utility by adopting a response that leads to the most favorable update of the community label. 2) The Opinion Formation Process involves the updating of an individual agent's opinion within a community-aware framework that incorporates bounded confidence. This process takes into account the updated matrix of community members and ensures that an agent's opinion aligns with the opinions of others within their community, within certain defined limits. The present study provides a theoretical proof that under any initial conditions, the aforementioned co-evolutionary dynamics process will ultimately reach an equilibrium state. In this state, both the opinion vector and community member matrix will stabilize after a finite number of iterations. In contrast to conventional opinion dynamics models, the guaranteed convergence of agent opinion within the same community ensures that the convergence of opinions takes place exclusively inside a given community.

Figures (15)

• Figure 1: (Left): The illustration of the difference between GCAOFP and LPA-HK on candidate strategy selection during the community dynamics process; (Right): Demonstration of the rationality of introducing the influence of inter-community neighbors into Eq. (\ref{['utility_define']}). We assume that the connections among agents are unweighted. The pairwise $\mathbf{E}_{ij}$ values associated with agent $i$ are marked in numbers, and the colors of nodes indicate their community labels.
• Figure 2: The boxplots of OSWG (100 implements) of GCAOFP on real-world networks. ($\lambda=1.4$ and $\psi=0.4$)
• Figure 3: The dynamics of agents' opinions of different dynamics models on Karate and PolBooks. The color of each opinion curve in each subplot indicates the community label of the corresponding agent obtained using different dynamics models.
• Figure 4: The dynamics of ACL of different dynamics models on Karate and PolBooks.
• Figure 5: The running time of different dynamics models with increasing number of links (Sorted by the number of links).

Theorems & Definitions (13)

• Definition 1
• Lemma 1
• Definition 2
• Theorem 1
• Theorem 2
• Theorem 3
• Definition 3
• Lemma 2
• Remark 1
• Lemma 3