Essays on Learning in Social Networks
Electrical and Electronics
Over the past few years, online social networks have become nearly ubiquitous, reshaping our social interactions as in no other point in history. The preeminent aspect of this social media revolution is arguably an almost complete transformation of the ways in which we acquire, process, store, and use information. In view of the evolving nature of social networks and their increasing complexity, development of formal models of social learning is imperative for a better understanding of the role of social networks in phenomena such as opinion formation, information aggregation, and coordination. This thesis takes a step in this direction by introducing and analyzing novel models of learning and coordination over networks. In particular, we provide answers to the following questions regarding a group of individuals who interact over a social network: 1) Do repeated communications between individuals with different subjective beliefs and pieces of information about a common true state lead them to eventually reach an agreement? 2) Do the individuals efficiently aggregate through their social interactions the information that is dispersed throughout the society? 3) And if so, how long does it take the individuals to aggregate the dispersed information and reach an agreement? This thesis provides answers to these questions given three different assumptions on the individuals' behavior in response to new information. We start by studying the behavior of a group of individuals who are fully rational and are only concerned with discovering the truth. We show that communications between rational individuals with access to complementary pieces of information eventually direct everyone to discover the truth. Yet in spite of its axiomatic appeal, fully rational agent behavior may not be a realistic assumption when dealing with large societies and complex networks due to the extreme computational complexity of Bayesian inference. Motivated by this observation, we next explore the implications of bounded rationality by introducing biases in the way agents interpret the opinions of others while at the same time maintaining the assumption that agents interpret their private observations rationally. Our analysis yields the result that when faced with overwhelming evidence in favor of the truth even biased agents will eventually learn to discover the truth. We further show that the rate of learning has a simple analytical characterization in terms of the relative entropy of agents' signal structures and their eigenvector centralities and use the characterization to perform comparative analysis. Finally, in the last chapter of the thesis, we introduce and analyze a novel model of opinion formation in which agents not only seek to discover the truth but also have the tendency to act in conformity with the rest of the population. Preference for conformity is relevant in scenarios ranging from participation in popular movements and following fads to trading in stock market. We argue that myopic agents who value conformity do not necessarily fully aggregate the dispersed information; nonetheless, we prove that examples of the failure of information aggregation are rare in a precise sense.