The Converse Consistency Principle in Bargaining

http://dx.doi.org/10.1006/game.2001.0907

The Converse Consistency Principle in Bargaining^*1

Youngsub Chun
School of Economics, Seoul National University, Seoul, 151-742, Korea^f1
Received 8 August 2000. Available online 18 June 2002.

Abstract

We investigate the implications of converse consistency in the context of bargaining. A solution is conversely consistent if, whenever, for some problem, a feasible alternative has the property that for all proper subgroups of the agents it involves, the solution chooses the restriction of the alternative to the subgroup for the associated reduced problem this subgroup faces, then the alternative should be the solution outcome for the problem. We present two alternative characterizations of the egalitarian solution based on converse consistency as well as either weak consistency or population monotonicity, in addition to other standard axioms of weak Pareto optimality, symmetry, and continuity. However, if we strengthen weak Pareto optimality to Pareto optimality, various impossibility results are obtained. On the other hand, the Nash solution is characterized on the basis of a weaker version of converse consistency, which applies its hypotheses only to the problem whose solution outcome is smooth.

Journal of Economic Literature Classification Numbers: C71, C78, D70.

Author Keywords: bargaining problem; converse consistency; egalitarian solution; Nash solution