Networks and collective action

Given a social network, we are interested in the problem of measuring the influence of a group of agents to lead the society to adopt their behavior. Motivated by the description of terrorist movements, we provide a markovian dynamical model for non-symmetric societies, which takes into account two special features: the hard core terrorist group cannot be influenced, and the remaining agents may change from active to non-active and vice versa during the process. In this setting, we interpret the absorption time of the model, which measures how quickly the terrorist movement achieve the support of all society, as a group measure of power. In some sense, our model generalizes the classical approach of DeGroot to consensus formation