AbstractsMathematics

In this dissertation we study emergent collective decision-making in social groups with time-varying interactions and heterogeneously informed individuals. First we analyze a nonlinear dynamical systems model motivated by animal collective motion with heterogeneously informed subpopulations, to examine the role of uninformed individuals. We find through formal analysis that adding uninformed individuals in a group increases the likelihood of a collective decision. Secondly, we propose a model for human shared decision-making with continuous-time feedback and where individuals have little information about the true preferences of other group members. We study model equilibria using bifurcation analysis to understand how the model predicts decisions based on the critical threshold parameters that represent an individual's tradeoff between social and environmental influences. Thirdly, we analyze continuous-time data of pairs of human subjects performing an experimental shared tracking task using our second proposed model in order to understand transient behavior and the decision-making process. We fit the model to data and show that it reproduces a wide range of human behaviors surprisingly well, suggesting that the model may have captured the mechanisms of observed behaviors. Finally, we study human behavior from a game-theoretic perspective by modeling the aforementioned tracking task as a repeated game with incomplete information. We show that the majority of the players are able to converge to playing Nash equilibrium strategies. We then suggest with simulations that the mean field evolution of strategies in the population resemble replicator dynamics, indicating that the individual strategies may be myopic. Decisions form the basis of control and problems involving deciding collectively between alternatives are ubiquitous in nature and in engineering. Understanding how multi-agent systems make decisions among alternatives also provides insight for designing decentralized control laws for engineering applications from mobile sensor networks for environmental monitoring to collective construction robots. With this dissertation we hope to provide additional methodology and mathematical models for understanding the behavior and control of collective decision-making in multi-agent systems.