Decision Making in Complex Environments: an adaptive network approach

In this thesis we investigate decision making in complex environments using adaptive network models. We first focus on the problem of consensus decision making in large animal groups. Each individual has an internal state that models its choice among the possible q alternatives and we assume that each individual updates its internal state using a majority rule, if it is connected to other individuals, or using a probabilistic rule. In this case, if the individual has no information, the choice shall be totally random, otherwise the probabilistic rule shall have a bias toward one of the q choices, measured by a parameter hi. The individuals shall also update their neighbourhood adaptively, which is modelled by a link creation/ link destruction process with an effective rate z . We show that the system, if there are no informed individuals, undergoes a I order phase transition at a give value, ∗z , between a disordered phase and a phase were consensus is reached. When the number of informed individuals increases, the first order phase transition remains, until one reaches a critical value of informed individuals above which the system is no more critical. We also prove that, for z in a critical range, the removal of knowledgeable individuals may induce a transition to a phase where the group is no able to reach a consensual decision. We apply these results to interpret some data on seasonal migrations of Atlantic Bluefin Tuna. We, then, build a model to describe the emergence of hierarchical structures in societies of rational self-interested agents. This model constitutes a highly stylised model for human societies. The decision-making problem of the agents, in this situation, is to which other agent to connect itself. We model the preference of agents of that society for connecting to more prominent agents with a parameter β. We show that there exists a sharp transition between a disordered equalitarian society and an ordered hierarchical society as beta increases. Moreover, we prove that, in a hierarchical society, social mobility is almost impossible, which captures behaviours that have been observed in real societies.