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Current policies directed at mitigating global warming appear unlikely to prevent temperatures from rising to levels that would trigger a precipitous increase in the costs of climate change. Various attempts at international cooperation to avoid this outcome have failed. Why is this problem so intractable? Can we expect an 11th-hour solution? Will some countries, or even all, succumb on the equilibrium path? We address these questions through a model that features the possibility of climate catastrophe and emphasizes the role of international externalities that a country's policies exert on other countries and intertemporal externalities that current generations exert on future generations. Within this setting, we explore the extent to which international agreements can mitigate the problem of climate change. Our analysis illuminates the role that international climate agreements can be expected to play in addressing climate change, and it points to important limitations on what such agreements can achieve, even under the best of circumstances