Coevolutionary dynamics of multidimensional opinions over coopetitive influence networks

To better understand opinion dynamics on social networks, especially when antagonistic interactions exist, we propose a novel coevolution model of multidimensional opinions and coopetitive (cooperative–competitive) influence networks. In this model, agents update their opinions according to the designed multidimensional Altafini-type rule. Additionally, the asynchronous evolutionary dynamics of influence networks is formulated based on three well-established sociological mechanisms: symmetry, influence, and person-opinion homophily. Going beyond the limitations of existing models in explaining network structural evolution, we characterize the sign equilibria of the influence dynamics as equivalent to all possible fully connected structurally balanced configurations, and prove that the influence networks will almost surely converge to sign equilibria within finite time. Further, we claim convergence of the opinion dynamics model and systematically analyze the role of the set of logic matrices in determining the limiting opinion distribution. For irreducible logic matrices, agents’ opinions on each topic exhibit a bipartite consensus under conditions of structurally balanced logic matrices and no competing logical interdependencies. For reducible logic matrices, the scope of opinions on a topic within an open strongly connected component (SCC) is determined by that of the closed SCCs it connects to. Finally, we provide simulation examples to illustrate the theoretical results.