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This article is concerned with situations in which avoiding a catastrophic outcome requires collective action. Using the logic of simple game theory, I identify circumstances that would cause rational players to act so as to guarantee that a catastrophe occurs, even when it is in their collective interests to avoid such an outcome – and when these players have the means at their disposal to ensure that such an outcome is avoided. I also identify circumstances that would cause rational players to act in concert to avert a catastrophe, and explain why other circumstances that might seem relevant to explaining these outcomes may be entirely inconsequential. Most of my discussion focuses on climate change. However, I also explain the relevance of the approach to three other areas: the millennium bug, drug resistance and nuclear arms control. In the final sections I discuss whether and how institutions might be designed to overcome, or at least reduce the likelihood of, catastrophic collective-action failures at the international level.