Bargaining Problems with Arbitrary Reference Points

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 then generalize the Tempered Aspirations solution (Balakrishnan, Gómez, and Vohra 2011) and study its properties in this new setting.