The article is devoted to the study of the phenomenon of homonymy and polysemy as one of the lexical varieties of the language game in the discourse of modern media. The purpose of the work is to present a picture of the realization of normal and occasional homonymy and polysemy as one of the methods of a language game. The combinatorial nature of language game is characterized by the creation of puns. Also the relations between the expression aspect and content aspect of the signs in the context frequently are realized in headlines of news and advertising texts, which contain language game. The uniqueness of a language game with homonymy (polysemy) consists in the fact that, being one of the simplest device in expression aspect, it allows to reproduce a complex interpretation mechanism and intertextuality of the text in content aspect.