  We consider two-person bargaining problems in which (only) the disagreement
outcome is private (and possibly correlated) information and it is common
knowledge that disagreement is inefficient. We show that if the Pareto frontier
is linear, the outcome 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 disagreement payoffs are independent or there is a player with at
most two types. We discuss implications of these results for axiomatic
bargaining theory and for full surplus extraction in mechanism design.
