La complexité d’un modèle simplifié d’interactions sociales : le modèle Léviathan

We propose an opinion dynamics model that combines processes
of vanity and opinion propagation. The interactions take place between
randomly chosen pairs. During an interaction, the agents propagate their
opinions about themselves and about other people they know. Moreover,
each individual is subject to vanity: if her interlocutor seems to value her
highly, then she increases her opinion about this interlocutor. On the contrary
she tends to decrease her opinion about those who seem to undervalue
her. The combination of these dynamics with the hypothesis that the opinion
propagation is more efficient when coming from highly valued individuals,
leads to different patterns when varying the parameters. For instance, for
some parameters the positive opinion links between individuals generate
a small world network. In one of the patterns, absolute dominance of one
agent alternates with a state of generalised distrust, where all agents have
a very low opinion of all the others (including themselves). We provide some
explanations of the mechanisms behind these emergent behaviors and finally
propose a discussion about their interest.