Complex systems approach to language games

The mechanisms leading language conventions to be socially accepted and adopted by a group are object of an intense debate. The issue can be of course addressed by different points of view, and recently also complex system science has started to contribute, mainly by means of computer simulations and analytical approaches. In this paper we study a very simple multi-agent model of convention spreading and investigate some of the crucial aspects of its dynamics, resorting, whenever possible, to quantitative analytic methods. In particular, the model is able to account for the emergence of global consensus out of local (pairwise) interactions. In this regard, a key question concerns the role of the size of the population. We investigate in detail how the cognitive efforts of the agents in terms of memory and the convergence time scale with the number of agents. We also point out the existence of an hidden timescale ruling a fundamental aspect of the dynamics, and we discuss the nature of the convergence process.