We explore how evolutionary game dynamics have to be modi"ed to accomodate a mathematical framework for the evolution of language. In particular, we are interested in the evolution of vocabulary, that is associations between signals and objects. We assume that successful communication contributes to biological "tness: individuals who communicate well leave more o!spring. Children inherit from their parents a strategy for language learning (a language acquisition device). We consider three mechanisms whereby language is passed from one generation to the next: (i) parental learning: children learn the language of their parents;
(ii) role model learning: children learn the language of individuals with a high payo!; and (iii) random learning: children learn the language of randomly chosen individuals. We show that parental and role model learning outperform random learning. Then we introduce mistakes in language learning and study how this process changes language over time. Mistakes increase the overall e$cacy of parental and role model learning: in a world with errors evolutionary adaptation is more e$cient. Our model also provides a simple explanation why homonomy is common while synonymy is rare.