  We study the classical bargaining problem and its two canonical solutions,
(Nash and Kalai-Smorodinsky), from a novel point of view: we ask for stability
of the solution if both players are able distort the underlying bargaining
process by reference to a third party (e.g. a court). By exploring the simplest
case, where decisions of the third party are made randomly we obtain a stable
solution, where players do not have any incentive to refer to such a third
party. While neither the Nash nor the Kalai-Smorodinsky solution are able to
ensure stability in case reference to a third party is possible, we found that
the Kalai-Smorodinsky solution seems to always dominate the stable allocation
which constitutes novel support in favor of the latter.
