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,
17z , 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
\u3b2. 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