Hobbes's own justification for the existence of governments relies on the assumption that without a government our lives in the state of nature would result in a state of war of every man against every man. Many contemporary scholars have tried to explain why universal war is unavoidable in Hobbes's state of nature by utilizing modern game theory. However, most game-theoretic models that have been presented so far do not accurately capture what Hobbes deems to be the primary cause of conflict in the state of nature—namely, uncertainty, rather than people's egoistic psychology. Therefore, I claim that any game-theoretic model that does not incorporate uncertainty into the picture is the wrong model. In this paper, I use Bayesian game theory to show how universal conflict can break out in the state of nature—even when the majority of the population would strictly prefer to cooperate and seek peace with other people—due to uncertainty about what type of person the other player is. Along the way, I show that the valuation of one's own life is one of the central mechanisms that drives Hobbes's pessimistic conclusion.