Social learning with bounded confidence and uninformed agents

This paper investigates a learning model in social networks with bounded confidence and uninformed agents. The neighboring relationships of agents are shaped by homophily in beliefs, which means any pair of agents are neighbors only if their belief difference is not larger than a positive constant, called bound of confidence. We consider two different kinds of agents: informed agents and uninformed agents, the essential difference between which is that informed agents are able to observe outside signals which can reflect the underlying true state. They update beliefs through Bayesian inference based on private signals plus consensus algorithm based on the beliefs of neighbors. Uninformed agents update their beliefs just by consensus algorithm without any inference. We find that the whole group can learn the true state only if the bound of confidence is larger than a positive threshold, which is related to the population density. Furthermore, we reveal that the larger the population density the smaller the proportion of informed agents needed to guide the group. By tuning the learning speed of informed agents, we find that the higher the speed, on the one hand, the shorter the time needed for the whole group to achieve steady state, but on the other hand, the lower the proportion of agents with successful learning, which is a trade-off.