A Coevolutionary Model for Actions and Opinions in Social Networks

In complex social networks, the decision-making mechanisms behind human actions and the cognitive processes that shape opinion formation processes are often intertwined, leading to complex and varied collective emergent behavior. In this paper, we propose a mathematical model that captures such a coevolution of actions and opinions. Following a discrete-time process, each individual decides between binary actions, aiming to coordinate with the actions of other members observed on a network of interactions and taking into account their own opinion. At the same time, the opinion of each individual evolves due to the opinions shared by other members, the actions observed on the network, and, possibly, an external influence source. We provide a global convergence result for a special case of the coupled dynamics. Steady state configurations in which all the individuals take the same action are then studied, elucidating the role of the model parameters and the network structure on the collective behavior of the system.