A noncooperative dynamic game model of opinion dynamics in multilayer social networks

Abstract

How do people living in a society form their opinions on daily or prevalent topics? A noncooperative di erential (dynamic) game model of opinion dynamics, where the agents' motives are shaped by how susceptible they are to others' in uence, how stubborn they are, and how quick they are willing to change their opinions on socially prevalent issues is considered here. The agents connected through a multilayer network interact with each other on a set of issues (layers) for a nite time duration. They express their opinions, listen to others' and, hence, mutually in uence each other. The tendency of agents to interact with people of similar traits, known as homophily, restricts them in their own localities, which may correspond to ethnicity but may as well be the ideological ones. This governs their interpersonal in uences and is the cause of clustering in the network. As the agents build their biases, they also create conceptions about the correlation between the issues. As a result, antagonistic interactions arise if the agents see each other as holding inconsistent opinions on the issues according to their individual conceptions. This way the interpersonal in uence becomes ine ective leading to con ict and disagreement between the agents. The dynamic game formulated here takes these subtle issues into account. The game is proved to admit a unique Nash equilibrium under a mild necessary and su cient condition. This condition is argued to be ful lled if there is some harmony of views among the agents in the network. The harmony may be in the form of similarity in pairwise conceptions about the issues but may also be a collective agreement on the status of a leader in the network. Since the agents do not seek any social motive in the game but their own individual motives, the existence of a Nash equilibrium can be interpreted as an emergent collective behavior out of the noncooperative actions of the agents.