Abstract
Opinion dynamics is the study of the exchange of opinions among agents embedded and communicating over a network. In particular, issues related to the formation of consensus of opinions, opinion clustering, and opinion influencing have drawn the attention of researchers in areas as diverse as sociophysics, economics, finance, computer science, and engineering, due to their potential application in social networks, marketing, cooperative control of autonomous agents, etc. In this dissertation, we utilize the Dempster-Shafer belief theoretic framework to capture agent opinions. The DS theoretic formulation allows us to account for the types of uncertainties that are inherent in social opinions in a more convenient and intuitive manner. Opinions that are modeled as probability mass functions (p.m.f.s) can also be captured as a special case of this belief theoretic formulation. The opinion exchange among neighboring agents are modeled using the Conditional Update Equation and the opinion exchange models adhere to notions in Social Judgment Theory which examines the basic psychological processes underlying the expression of attitudes and their modifiability through communication. To study consensus and opinion clustering with this belief theoretic viewpoint, we take two different approaches. In the first approach, using matrix theoretic analysis, we introduce the notion of opinion dynamic chains to account for opinions that are modeled as p.m.f.s. In particular, we explore how the presence of opinion leaders affects consensus and opinion cluster formation. This analysis however assumes synchronous (i.e., delay-less) communication between agents. In the second approach, we utilize notions from paracontractions theory to account for ad-hoc and dynamic networks with possibly asynchronous message passing. With agents embedded within such an ad-hoc, dynamic, and asynchronous network structure, and agent opinions captured via the more general DS belief theoretic models, conditions under which consensus and opinion clustering occur are explored, giving special attention to the presence of opinion leaders. Another aspect of the work undertaken in this dissertation is how to generate a network in order for the agents to reach a consensus. In particular, given the agent opinion distribution and the bound of confidence, we determine the edge formation probability among agents in an Erdos-Renyi random network. The ultimate objective is to build the network topology for consensus-based distributed decision making.