In recent years, we have observed an increased interest within the field of design research in both the concept of conviviality and playful approaches as a pathway to co-design and participation. While play is often associated with freedom of expression and creativity, the implication of rules and mechanics in games poses questions regarding the tension between player agency and designed gameplay. This paper aims to provide reflection on these topics through a lens of ‘critical play’ and presents a model to explore games’ potential as convivial tools for imagining collective futures.