Monotonicity of bargaining solutions with respect to the disagreement point

We investigate whether the best known solutions to the bargaining problem respond appropriately to certain changes in the disagreement point d, for a fixed feasible set. If d_i increases, while for each j ≠ i, d_j remains constant, then these solutions recommend an increase in agent i's payoff, in agreement with intuition. However, the stronger requirement that agent i be the only one to gain is not generally met.