Endogenous control of DeGroot learning

Abstract

The DeGroot update cycle for belief learning in social networks models beliefs as convex combinations of older beliefs using a stochastic matrix of social influence weights. In this paper, we explore a new endogenous control scenario for this type of learning, where an agent on her own initiative, adjusts her private social influence to follow another agent, say, one which receives higher attention from other agents, or one with higher beliefs. We develop an algorithm which we refer to as BLIFT, and show that this type of endogenous perturbation of social influence can lead to a 'lifting' or increasing of beliefs of all agents in the network. We show that the per-cycle perturbations produce improved variance contractions on the columns of the stochastic matrix of social influences, resulting in faster convergence, as well as consensus in beliefs. We also show that this may allow belief values to be increased beyond the DeGroot beliefs, which we show are the lower bounds for BLIFT. The result of application of BLIFT is illustrated with a simple synthetic example. © 2011 Springer-Verlag.