Language emergence and evolution has recently gained growing attention through multiagent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding. 15:56 WSPC/INSTRUCTION FILE ng˙long˙ijmpc˙last3 2 Andrea Baronchelli, Vittorio Loreto and Luc Steels telepathy? The problem has been addressed by several disciplines, but it is only in the last decade that there has been a growing effort to tackle it scientifically using multi-agent models and mathematical approaches (cfr. 1,2,3 for a review). Initially these models focused on the emergence of a shared vocabulary, but increasingly attempts are made to tackle grammar 1,4,5,6,7 .The proposed models can be classified as defending a sociobiological or a sociocultural explanation. The sociobiological approach 8 , which includes the evolutionary language game 1 , is based on the assumption that successful communicators, enjoying a selective advantage, are more likely to reproduce than worse communicators. If communication strategies are innate, then more successful strategies will displace rivals. The term strategy acquires its precise meaning in the context of a particular model. For instance, it can be a strategy for acquiring the lexicon of a language, i.e., a function from samplings of observed behaviors to acquired communicative behavior patterns 8,9,10 , or it can simply coincide with the lexicon of the parents 1 or with some strong disposition to acquire a particular kind of syntax, usually called innate Universal Grammar 11 .In this paper we discuss a model, first proposed in 12 , that belongs to the sociocultural family 13,14,15 . Here, good strategies do not necessarily provide higher reproductive success, but only higher communicative success and greater expressive power, and hence greater success in reaching cooperative goals, with less effort. Agents select better strategies exploiting cultural choices, feedback from communication, and a sense of effort. Agents have not only the ability to acquire an existing system but to expand their rules to deal with new communicative challenges and to adjust their rules based on observing the behavior of others. Global coordination emerges over cultural timescales, and language is seen as an evolving and self-organized system 16 . While the sociobiological approach emphasizes language transmission following a vertical, genetic or generational line, the sociocultural approach emphasizes peer-to-peer interaction 17 .A second, fundamental distinction among the different models concerns the adopted mechanisms of social learning describing how stable dispositions are ...