Designing social networks for efficient learning

We study structural properties for information aggregation in settings where selfinterested agents take actions sequentially and partially observe each other. Agents optimize their choice of action based on some local information (or ‘private signal’) as well as conclusions they draw from observing actions taken by others. The literature so far typically studies the case where all agents observe each other. In such a setting it has been shown that information need not be aggregated and agents run a risk of herding on an inferior action. The other extreme, where agents do not observe each other at all clearly will not allow for social learning. In this paper we study the interim case where agents partly observe each other. We model partial observability by overlaying a graph structure over the agents. We consider the challenge of designing such a network structure that guarantees social learning. We introduce the ‘celebrity graph’ and prove that it induces social learning and an optimal outcome with overwhelming probability. We study variations of this setting which depend on our assumption over the order or arrival of the agents (Bayesian and adversarial).