Social Learning over Weak Graphs

In this dissertation, we study diffusion social learning over weakly-connected graphs and reveal several interesting properties characterizing the flow of information over such networks. We discover that the asymmetric flow of information hinders the learning ability of certain agents regardless of their local observations. Under some circumstances that we clarify in this work, a scenario of total influence (or "mind-control") arises where a set of influential agents ends up shaping the beliefs of non-influential agents. We derive useful closed-form expressions that characterize this influence, and then analyze this control mechanism more closely to highlight some critical properties. In particular, we use the theoretical analysis to address two main questions: (a) First, how much freedom do influential agents have in controlling the beliefs of the receiving agents? That is, can influential agents drive receiving agents to arbitrary beliefs or does the network structure limit the scope of control by the influential agents? and (b) second, even if there is a limit to what influential agents can accomplish, how can they ensure that receiving agents will end up with particular beliefs? These questions raise interesting possibilities about belief control. Once addressed, we end up with design procedures that allow influential agents to drive other agents to endorse particular beliefs regardless of their convictions. We illustrate the theoretical findings and results by means of several examples and numerical simulations