This paper studies a simplified version of the Leviathan model, without gossip and vanity processes. During dyadic meetings, the agents change their opinion about themselves and about their interlocutor. Speakers highly valued by their listeners are more influential. Only due to the asymmetry of the influence function, the model produces several patterns depending on the parameter values, some of which not yet identified in the first Leviathan model study. In particular, in some cases the leaders have a high opinion of other leaders whereas in other cases they have a low one