Two-person bargaining when the disagreement point is private information

We consider two-person bargaining problems in which (only) the disagreement payoffs are private information and it is common knowledge that disagreement is inefficient. We show that, in the NTU-case, if the Pareto frontier is linear, the players' interim utilities of an ex post efficient mechanism cannot depend on the disagreement payoffs. If the frontier is non-linear, the result continues to hold when the conflict payoffs are independent, or one player has at most two types. In the TU-case, a similar independence result holds for ex post efficient mechanisms that are individually rational, provided the players' budgets satisfy a certain condition. We discuss implications of these results for axiomatic bargaining theory, surplus extraction by an informed principal and egalitarian mechanisms.