Following vartiainen (2007) we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical kalai–smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain.
Bozbay, I., Dietrich, F. K., & Peters, H. J. M. (2012). Bargaining with endogenous disagreement: the extended Kalai-Smorodinsky solution. Games and Economic Behavior, 74(1), 407-417. https://doi.org/10.1016/j.geb.2011.06.007