Bargaining Problems with a Salient Point

A number of authors have enriched Nash’s original bargaining problem through the introduction of an additional point, which we call a salient point. When the salient point is restricted to lie in the bargaining set, it is interpreted as a reference point, the outcome, perhaps, of a bargain from an earlier period. When restricted to lie outside the bargaining set, it is interpreted as a claim on the resources being shared. Here we remove the restriction that the salient point must lie either in or outside the bargaining set to obtain a new model we call the Bargaining Problem with a Salient Point. We propose and axiomatically characterize a solution for this bargaining problem. It generalizes Chun and Thomson’s (1992) Proportional solution to problems in which the salient point lies in the bargaining set. When utility is transferable, our solution can be interpreted as a compromise between the Kalai Smorodinsky solution and the weighted (according to the salient point) Nash Bargaining solution.