  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.
