Bipartite consensus of concatenated opinion dynamics for two antagonistic groups: A game theoretical perspective

Recent decades have witnessed a significant surge in scholarly attention towards formulating dynamic models for opinion formation on social networks. This paper considers the bipartite consensus problem over a series of issues for two antagonistic groups wherein two graphs are employed to model the interaction within groups and a noncooperative game to describe the interaction between groups. Firstly, we prove that the noncooperative game admits the unique Nash equilibrium. Secondly, we give sufficient conditions for achieving a bipartite consensus that both graphs are strongly connected. Additionally, we obtain that the game's mechanism decides the convergence rate of bipartite consensus from one issue to the next. It is important to highlight that confrontation is key in elevating the most influential individuals to leadership positions within their groups. Thirdly, we construct the bipartite consensus state for a particular case where the networks of two groups are balanced. Finally, we present two examples to demonstrate the theoretical results.