Analysis of threshold models for collective actions in social networks

In this paper, we study the asymptotic behaviors of threshold models used to describe the formation of collective actions in social networks. At each time instant, each agent of the network makes a choice between two possible actions. The decision is made on the basis of the actions chosen by its neighbors and the value of a dynamically updated threshold. The main novelty of the proposed model is the introduction of a parameter accounting for the level of self-confidence of the agents, which affects the dynamic evolution of the threshold and in turn the way the agents make their decision. The objective is to identify which are the possible limiting behaviors of the network and under which conditions each of them occurs. Three different network topologies are considered. In the case of complete graph, the asymptotic behaviors are analytically characterized, whereas for star and ring graphs an extensive numerical analysis is presented.