A new insight into three bargaining solutions in convex problems

at the Andrew Young School of Policy Studies

"A new insight into three bargaining solutions in convex problems" (pdf)

by Yongsheng Xu and Naoki Yoshihara
April 2004

Keywords: Nash solution, Kalai-Smorondinsky solution, egalitarian solution, bargain problem, expansion independence, contraction independence

We reconsider the three well-known solutions: the Nash, the egalitarian and the Kalai-Smorodinsky solutions, to the classical domains of convex bargaining problems. A new proof for the Nash solution that highlights the crucial role the axiom Contraction Independence plays is provided. We also give new axiomatic characterizations for both the egalitarian and the Kalai-Smorodinsky solutions. Our results focus on both contraction and expansion independence properties of bargaining problems and, as a consequence, some new insights on the three solutions from the perspective of rational choice may be derived.

Comments and questions regarding this paper may be directed to Yongsheng Xu at yxu3@gsu.edu.