Exogenous control of DeGroot belief learning

Abstract

Belief learning in social networks is thought to occur through an update process that aggregates dispersed information on the beliefs of connected neighbors through social influences. We explore mechanisms to apply persuasive biases to beliefs at the individual and group level, using the popular DeGroot update as the basic network-learning scheme, to achieve purposeful control on belief learning. We show that linear control of belief learning results in the possibility of shaping the beliefs of individual agents. We prove convergence of the control and show that external persuasive biases, which are our linear control parameters, are not only learnt by the agents just as they learn beliefs, but they can even swamp out the original beliefs. We establish the theoretical foundation for linear dynamic control of belief learning in this paper and illustrate the key results with examples of small networks which show how emerging consensus can be amplified or even destroyed.