Nash bargaining solution under predonation

Abstract

We consider two person bargaining problems under predonation. Before the bargaining solution is applied we allow the alteration of the bargaining set by means of pre-donations of a share in one’s would-be payoffs to one’s opponent. Thus, a pre-bargain stage is instituted in which the bargainers may manipulate, via pre-donations, the (Nash) bargaining solution as applied in the next stage.We firstly concentrate on the simple bargaining problems with bargaining sets that have linear pareto frontier and show that the stronger bargainer (with greater ideal payoff) giving a pre-donation, her best pre-donation transforming the bargaining set into one on which the Nash bargaining solution distributes payoffs so that while other bargainer gets exactly the same payoff (as applied to the original simple bargaining problem), stronger bargainer makes strictly better off. Then, we look for Stackelberg and Nash equilibria of the so called ”predonation game”. Furthermore, we list our results for two by two normal form games.