Can stubbornness or gullibility lead to faster consensus? A study of various strategies for reaching consensus in a model of the naming game

The naming game is a dynamical system that is used to model and study language formation, in particular to determine how words are formed that are used by all members of a community to denote the same object or concept. We propose a model of the naming game that allows for theoretical investigation under various behavior for agent interaction. In particular, we give conditions on the network such that consensus is reached where at most p synonyms are used to describe a single object. In addition, we give lower bounds on the convergence rate to consensus. Furthermore, we study various agent interaction behaviors and their effect on the time needed to reach consensus. We show that even though a democratic strategy is in general the best strategy for reaching consensus, a stubborn or a gullible strategy can allow for faster word formation than a democratic strategy for certain connection topologies among the agents.