Game theory has proven useful in clarifying Hobbes’s argument that the state of nature will inevitably devolve into a state of war. Mathematically-leaning philosophers, however, have paid little attention to Rousseau’s depiction of the state of nature as a peaceful, asocial state of solitary wanderers. This paper articulates Rousseau’s critique of Hobbes in formal terms, which pinpoints two crucial issues in Hobbes’s account: the lack of an exit option and an unrealistic depiction of human nature. Building upon recent game-theoretic treatments (...) of Hobbes, we first construct a model that incorporates Rousseau’s criticisms by permitting an exit option and endogenizing human preferences and capacities. Second, we draw out the implications of Rousseau’s analysis for the question of political authority, which cannot be answered, as Hobbes believed, by invoking a hypothetical state of nature. (shrink)