We propose a solution to the bargaining problem which responds appropriately to certain changes in the disagreement point, for a fixed feasible set. If di increases, while for j=/i, dj remains constant, our solution recommends an increase in agent i's payoff, in agreement with intention. We also show that an increase in risk aversion is to the player's own advantage and to the disadvantage of the opponent in the two person case; to the disadvantage of all opponents in the multi-person generalization.