Game Theory Based Community-Aware Opinion 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.