Phase transition and fast agreement in Naming Game with preference for multi-word agents

We examine a variant of the Naming Game, where agents having several words communicate more often than single-word agents. Depending on the preference and dimensionality, the model either converges to a single-language state as in an ordinary Naming Game or remains in a disordered, multi-language phase. At the transition point separating these regimes, due to a percolation-like process, the model converges to a single-language state but much faster than in the ordinary naming game. We also show that the coarsening dynamics of the ordinary Naming Game is slower than expected due to stripe structures that sometimes spontaneously form during the evolution of the model.