Endogenous control of DeGroot belief learning
Our focus in this paper is to study a specific type of imitative behavior in the framework of non-Bayesian models, and to endow it with an endogenous control mechanism aimed at modeling a leader-following behavior. We show how an agents assertion of endogenous control in a social network is learned dynamically by the other agents in the course of their interactions. We develop variants of the DeGroot algorithm which we call BLIFT to illustrate two scenarios which lead to completely different situations. We illustrate how control could be related to changes in the social influence weights and how its manipulation could lead to a general consensus or homophily in a network. We show the convergence of the two algorithms and analyze their theoretical properties. We construct synthetic examples to illustrate our two methods.
endogenous control belief learning imitative behavior social networks degroot model