Accelerating Consensus by Preferential Words in the Naming Game

The naming game is a model of nonequilibrium dynamics for the self-organized emergence of a language or a communication system. We study a modified version of the minimal naming game in which the speaker selects a word from its inventory with a probability proportional to exp(R_s*α), where R_s is the success ratio of the name and α is a tunable parameter. By investigating the effects of α on the evolutionary processes for both square lattice and scale−free networks, we find that the convergence time decreases with the increasing α on both two networks, which indicates that preferential selection of successful words can accelerate the reaching of consensus. More interestingly, for α>0, we find that the relation between convergence time and α exhibits a power-law form.