This paper presents and solves a crisis bargaining game under limited information. The sides alternate offers from three possible offers, with war and its costs starting if the target's counteroffer is rejected. The equilibrium of the model falls into four different cases. These four cases are analyzed to determine how the sides communicate through their offers and how the costs of war, initial beliefs, misperceptions, and distribution of capabilities drive the probabilities of a crisis and war. The model demonstrates a joint selection bias-misspecification problem in empirical studies of crises arising from the unobservable nature of beliefs. Several empirical studies of crisis bargaining are discussed in the light of this methodological problem, new patterns of evidence are found that support the presence of the selection problem, and their conclusions are reexamined.