The model is based on the influence function of the Leviathan model (Deffuant, Carletti, Huet 2013 and Huet and Deffuant 2017) with the addition of group idenetity. We aim at better explaining some patterns generated by this model, using a derived mathematical approximation of the evolution of the opinions averaged.

We consider agents having an opinion/esteem about each other and about themselves. During dyadic meetings, agents change their respective opinion about each other, and possibly about other agents they gossip about, with a noisy perception of the opinions of their interlocutor. Highly valued agents are more influential in such encounters. Moreover, each agent belongs to a single group and the opinions within the group are attracted to their average.

We show that a group hierarchy can emerges from this model, and that the inequality of reputations among groups have a negative effect on the opinions about the groups of low status. The mathematical analysis of the opinion dynamic shows that the lower the status of the group, the more detrimental the interactions with the agents of other groups are for the opinions about this group, especially when gossip is activated. However, the interactions between agents of the same group tend to have a positive effect on the opinions about this group.