Social learning with uninformed agents: Convergence and efficiency

Almost all existing social learning models assume that each agent can perceive her private signal which is used in updating her belief. In this work, we assume that there are some uninformed agents in the network which cannot observe their private signals and update their beliefs just based on the beliefs of their neighbors. We prove that under mild assumptions, even one informed agent is enough to lead all agents in the network eventually learn the true state of the world almost surely. Furthermore, we show through simulation that in a heterogeneous undirected network, it is more efficient to have a few hub agents as the informed agents which can observe their signals, and the convergence speed is almost the same as that when all agents are informed agents.