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The model is based on the influence function of the Leviathan model (Deffuant, Carletti, Huet 2013 and Huet and Deffuant 2017). 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.
We show that the inequality of reputations among agents have a negative effect on the opinions about the agents of low status.The mathematical analysis of the opinion dynamic shows that the lower the status of the agent, the more detrimental the interactions are for the opinions about this agent, especially when gossip is activated, while the interactions always tend to increase the opinions about agents of high status.