Coevolution of actions and opinions in networks of coordinating and anti-coordinating agents

In this paper, we investigate the dynamics of coordinating and anti-coordinating agents in a coevolutionary model for actions and opinions. In the model, individuals in a population interact on a two-layer network, sharing their opinions and observing others’ actions, while revising their own opinions and actions according to a game-theoretic mechanism grounded in social psychology literature. First, we consider the scenario of coordinating agents, where convergence to a Nash equilibrium (NE) is guaranteed. We identify conditions for reaching consensus configurations and establish regions of attraction for these equilibria. Second, we study networks of anti-coordinating agents. Here, we prove that all trajectories converge to an NE by leveraging potential game theory. Then, we establish analytical conditions on the network structure and model parameters to guarantee the existence of consensus and polarized equilibria, characterizing their regions of attraction.