By collaborating with others, humans can pool their limited knowledge, skills, and resources to achieve goals that outstrip the abilities of any one person. What cognitive capacities make human collaboration possible? Here, we propose that collaboration is grounded in an intuitive understanding of how others think and of what they can do—in other words, of their mental states and competence. We present a belief–desire–competence framework that formalizes this proposal by extending existing models of commonsense psychological reasoning. Our framework predicts that agents recursively reason how much effort they and their partner will allocate to a task, based on the rewards at stake and on their own and their collaborator’s competence. Across three experiments (N = 249), we show that the belief–desire–competence framework captures human judgments in a variety of contexts that are critical to collaboration, including predicting whether a joint activity will succeed (Experiment 1), selecting incentives for collaborators (Experiment 2), and choosing which individuals to recruit for a collaborative task (Experiment 3). Our work provides a theoretical framework for understanding how commonsense psychological reasoning contributes to collaborative achievements.