Working with the definition of mutual optimism as war due to inconsistent beliefs, we formalize the mutual optimism argument to test the theory's logical validity. We find that in the class of strategic situations where mutual optimism is a necessary condition for war—i.e., where war is known to be inefficient, war only occurs if both sides prefer it to a negotiated settlement, and on the eve of conflict war is self-evident—then there is no Bayesian-Nash equilibrium where wars are fought because of mutual optimism. The fundamental reason that mutual optimism cannot lead to war is that if both sides are willing to fight, each side should infer that they have either underestimated the strength of the opponent or overestimated their own strength. In either case, these inferences lead to a peaceful settlement of the dispute. We also show that this result extends to situations in which there is bounded rationality and/or noncommon priors.