In this paper a dialogue game for critical discussion is developed. The dialogue game is a formalisation of the ideal discussion model that is central to the pragma-dialectical theory of argumentation. The formalisation is intended as a preparatory step to facilitate the development of computational tools to support the pragma-dialectical study of argumentation. An important dimension of the pragma-dialectical discussion model is the role played by speech acts. The central issue addressed in this paper is how the speech act perspective can be accommodated in the formalisation as a dialogue game. The starting point is an existing ‘basic’ dialogue game for critical discussion, in which speech acts are not addressed. The speech act perspective is introduced into the dialogue game by changing the rules that govern the moves that can be made and the commitments that these result in, while the rules for the beginning, for the end, and for the structure of the dialogue game remain unchanged. The revision of the move rules is based on the distribution of speech acts in the pragma-dialectical discussion model. The revision of the commitment rules is based on the felicity conditions that are associated with those speech acts.