Topics in Sequential Decision Making: Analysis and Applications

Interest in group decision making spans a wide variety of domains. Be it in electoral votes in politics, Bayesian learning in social networks, distributed detection in robotic and sensor networks, or cognitive data processing in the human brain, establishing the best strategy or understanding the motivation behind an observed strategy, has been of interest for many researchers. This thesis studies two sequential decision making problems, in the first problem the individuals do not communicate with each other, while in the second problem they are allowed to exchange information.;In the non-cooperative setting, we consider a collection of agents, each performing binary hypothesis testing and obtaining a decision over time. We assume that the agents are identical and receive independent information. Individual decisions are sequentially aggregated via a threshold-based rule. In other words, a collective decision is taken as soon as a specified number of agents report a concordant decision (simultaneous discordant decisions and no-decision outcomes are also handled). We relate the accuracy and decision time of the whole population, to the accuracy and decision time of a single individual and to the fusion rule. We also provide a scalability analysis for some group decision rules and show that in the limit of large group sizes, the accuracy and decision time of the group are dictated by the accuracy and decision time of a single individual.;In the cooperative setting, a group of individuals are monitoring an environment and answering a question about the location of a source. The environment is divided into smaller regions of responsibilities, each individual is responsible for one or multiple regions. We pose the problem as a multiple hypothesis testing problem and design a distributed sequential localization algorithm with guaranteed accuracy bounds; we also provide a proof of almost sure convergence of our algorithm in the limit of a large numbers of measurements. We pose and distributedly solve optimization problems whose solution provides a choice of regions that improves the performance of the localization algorithm. We illustrate the applicability of the proposed distributed optimization algorithm to a family of optimization problems.