In this thesis, we mainly introduce two models. First, we introduce a model of social learning in which agents share true and false signals with different de-cays and to different people. Our results establish that these asymmetries, thus far largely ignored in theory despite being empirically observed, determine the long-run beliefs of a society. The agents who are more central in the network of negative signals sharing are more prone to be misinformed. We derive a single threshold condition under which societies reach the true state or are mis-informed in the long run. Additionally, we derive the speed of convergence to a given state, which is crucial for decision-making constrained by time. Both the threshold condition and speed of convergence depend on the combina-tion of network structure, as measured by the largest eigenvalue of the adja-cency matrix, and the decay factors, but are largely independent of the initial distribution of signals. We illustrate these results using numerical simulations that incorporate societies segmented into groups and discuss policy implications.

Second, we focus on an opinion formation model over the signed networks. We assume that the network nodes are of two different types and link signs correlate with the node types, which induces some patterns of structural bal-ance. Given a signed network and information on the type of some source nodes, we consider an observer outside the network who attempts to judge the type of a given target node. Computing the globally optimal belief by Bayes’ rule involves considering exponentially many states. We propose a much simpler heuristic that is based on the shortest paths between source nodes and target nodes. Theoretically, this heuristic is weakly better than an-other heuristic from the literature and it coincides with the Bayesian rule when the shortest paths between the source nodes and a target node are unique and non-overlapping. With simulations, we assess the accuracy of these three rules and find that differences can be substantial. The shortest path heuristic is better than the other heuristic in handling multiple source nodes, even though it aggregates information suboptimally. The crucial network statistic for accu-racy is the average distance in a network.