Towards a Common Lexicon in The Naming Game: The Dynamics of Synonymy Reduction

In this paper we introduce a mathematical model of naming games, named the sampling-amplification model. Naming games have been extensively used to investigate the dynamics of lexicon acquisition. Despite the many interesting empirical results these studies have produced, most of this research lacks a formal (realistic) elucidating theory. In this paper we try to bridge the gap between mathematical models and empirical studies of naming games in a novel manner, differing from existing work in two important ways: One, we relax the too strong assumption that the game is sampled infinitely often during each time interval. This assumption is usually made to guarantee convergence of an empirical learning process to a deterministic dynamical system. Although the dynamical system will predict the learning process approximately well, it cannot be considered a realistic setting as infinitely sampling does not occur in the real world. Two, we provide a proof that under these new realistic conditions, our model converges to a common language for the entire population of agents. Finally the model is experimentally validated.