In this paper we introduce a mathematical model of naming games. Naming games have been widely used within research on the origins and evolution of language. Despite the many interesting empirical results these studies have produced, most of this research lacks a formal elucidating theory. In this paper we show how a population of agents can reach linguistic consensus, i.e. learn to use one common language to communicate with one another. Our approach differs from existing formal work in two important ways: one, we relax the too strong assumption that an agent samples infinitely often during each time interval. This assumption is usually made to guarantee convergence of an empirical learning process to a deterministic dynamical system. 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.
DeVylder, B., & Tuyls, K. P. (2006). How to Reach Linguistic Consensus: A Proof of Convergence for the Naming Game. Journal of Theoretical Biology, 242(4), 818-831. https://doi.org/10.1016/j.jtbi.2006.05.024