Egalitarian–utilitarian bounds in Nash’s bargaining problem

Abstract

For every 2-person bargaining problem, the Nash bargaining solution selects a point that is "between" the relative (or normalized) utilitarian point and the relative egalitarian (i.e., Kalai-Smorodinsky) point. Also, it is "between" the (non-normalized) utilitarian and egalitarian points. I improve these bounds. I also derive a new characterization of the Nash solution which combines a bounds property together with strong individual rationality and an axiom which is new to Nash's bargaining model, the sandwich axiom. The sandwich axiom is a weakening of Nash's IIA.

The Nash bargaining solution: sometimes more utilitarian, sometimes more egalitarian

“…1;2 In a previous paper, Rachmilevitch (2015), I provided an alternative proof of the aforementioned betweenness. In that paper, as well as in Rachmilevitch (2016), I showed that the Nash solution, in several senses, is closer to utilitarianism than it is to egalitarianism. In particular, I showed how the portion of the Pareto frontier that ranges from the utilitarian point to the egalitarian point can be meaningfully divided into two parts, and the Nash point lies in the part closer to the utilitarian choice.…”

Modeling household relocation choice: An egalitarian bargaining approach and a comparative study

“…Therefore, it balances fairness and efficiency, which is a tradeoff and compromise between egalitarianism and utilitarianism. Moreover, the Nash bargaining solution is demonstrated to be more utilitarian than egalitarian (Rachmilevitch, 2016). That is, it puts more emphasis on utilitarianism than egalitarianism.…”

“…It is based on the principle of maximizing the product of players' surplus utilities, applicable to bargaining scenarios when negotiators with personal preferences are motivated to achieve proportionate cooperation (MacCrimmon & Messick, 1976). The Nash bargaining solution is "between" the utilitarian and egalitarian points (Rachmilevitch, 2016). Therefore, it balances fairness and efficiency, which is a tradeoff and compromise between egalitarianism and utilitarianism.…”

“…It is later noticed and analyzed by researchers that the additive formulation only deals with the efficiency of group's choice (utilitarianism philosophy), without capturing group's equity concern for fair distribution of benefits among group members (Diamond, 1967;Keeney & Kirkwood, 1975). That is why the corresponding solution is called (weighted) utilitarian solution (Hinojosa & Mármol, 2011;Argenziano & Gilboa, 2015;Rachmilevitch, 2015Rachmilevitch, , 2016.…”