Bargaining under Almost Complete Information

It is well-established that in bargaining under complete information, two agents reach an agreement immediately. I assume that nature selects a state that favors one or the other, and the agents may not know the state with probability ε, inducing higher- order uncertainty. A unique equilibrium emerges, resembling a war of attrition. Given the bargaining environment, as ε → 0, in equilibrium, in all states, agents almost immediately agree as they do under complete information. However, this convergence is not uniform. Given ε (however small), one can find a bargaining environment where immediate agreement is impossible in one state or the other