Relative responsiveness of bargaining solutions to changes in status-quo payoffs

It is a well-known fact that several prominent bargaining solutions are responsive to changes in status-quo (i.e., disagreement or fallback) payoffs. When an agent’s status-quo payoff increases, his solution payoff either stays the same or increases. A fully general result for these solutions’ status-quo point ranking is impossible to establish. In this paper, using an important class of bargaining problems, a ranking of the relative status-quo point responsiveness of prominent bargaining solutions is obtained. Using the Constant Elasticity of Substitution class of bargaining problems, regardless of the concavity of the Pareto frontier and the level of increase in one’s status-quo payoff, we find the equal gains solution is the most responsive with respect to changes in status-quo payoffs, followed by the Nash solution. The equal sacrifice solutions is the least responsive, followed by the Kalai/Smorodinsky solution.