Non-Bayesian Social Learning

Abstract

We explore the problem of a network of nodes attempting to learn some underlying parameter by observing signals and sharing their beliefs with each other. We look in particular at the problem proposed by Jadbabaie et al. (2012), in which nodes share their beliefs with their neighbors and update their beliefs at each time step based on the beliefs of their neighbors (using naive averaging), and based on a private information signal that they receive at each time step (using Bayesian updating). We look at convergence time in several simple examples. We investigate the difference in convergence time resulting from adding a delay to the time until nodes can see the beliefs of their neighbors, as well as the difference in convergence time resulting from preventing nodes from seeing their neighbors' beliefs at all.