A cooperative group activity (CGA) and shared intentionality are two phenomena whereby two or more individuals engage in an activity with the intention that the group will succeed, that is, to act as a “we. ” This ability to act together as a “we” is an important human psychological feature and has been argued to demarcate an important developmental step. Many CGA and shared intentionality theories have centered around philosophical problems of what counts as a “we” and how to give a cognitively plausible account of children's engagement in such activities, e.g., pretend play by toddlers. The aims of this paper are (i) to highlight the importance of distinguishing between creating and sustaining a CGA, since they require different cognitive abilities, (ii) to give a cognitively plausible account of the creation of a CGA, and iii) to present a formal framework of the sustainability of a CGA that can illuminate how engagement in a CGA stimulates cognitive change in its members. In the first part (section Creating cooperative group activity) of the paper, several theoretical problems are discussed, including the common knowledge problem, the jointness problem, the central problem, and the cognitively plausible explanation problem. The section ends with a cognitively plausible account of the creation of a CGA. The second part (section Sustainability of cooperative group activity) of the paper presents a formal framework of belief compatibility and trust relations. It explores how engagement in a CGA places certain cognitive constraints on its members while stimulating cognitive change and development. The paper ends with a discussion of empirical postulations derived from this account.