Games have been used in civic participation (Lerner, 2014) and civic learning (Raphael et al. 2010). Building on the idea of using games for participation, democracy and collaboration, we propose approaching games as tools for convivial learning. First introduced by Illich (1973), the concept of conviviality envisions a society characterised by collaboration and self-determination, underpinned by tools that encourage joyful interaction, creativity and human agency through control over the tools. We believe that games as convivial tools could help bring forth creativity and mutual learning about civic processes and desirable futures. Yet, games’ nature as rigid systems of rules (Salen & Zimmerman, 2010) seems potentially at odds with positioning them as tools promoting agency. We propose to use the tension arising between rigidity and agency as starting point for exploring game design strategies for convivial games through research-through-design. We ask how games for thinking about the future may be designed that allow players to exercise control over their own experience, and to what effect. Inspired by the concept of critical play (Flanagan, 2009; Grace, 2014) and building on the distinction between narrative and mechanics as key constituting game elements, we have designed two distinct games for collaboratively engaging with the future. The first, Narrate, focuses on letting players invent their own narrative, whilst the second game Remix allows for experimentation with game rules and mechanics. We present the design process for each game and contrast the different approaches taken. Each game was tested by two groups and analysed in regards to its capacity to bring forth conviviality, creativity and collaboration. The paper compares and provides a discussion on how suitable the two chosen strategies of experimenting with narrative or mechanics are for (1) facilitating thinking and learning about shared futures, and (2) supporting player agency and bringing forth convivial interactions.