Learning under social influence

In this paper, we study a model of social learning where individuals are under influence of others in their social clique. In our model, each agent receives private noisy signals about an unobservable, underlying state of the world. At the end of each time period, the belief of an individual is equal to the convex combination of her posterior beliefs derived from the signal observed, and the priors of her neighbors. Our model reduces to the well-known consensus model when private signals are non-informative. We show that if the network of social influences is strongly connected, then all agents will have asymptotically correct forecasts. In other words, all individuals will be able to asymptotically learn the true state of the world, as far as their observations are concerned. Finally, we show that all agents assign asymptotically equal beliefs to the true state of the world.