Review of Economic Design

, Volume 16, Issue 4, pp 269–282

Nash bargaining in ordinal environments

Original Paper

DOI: 10.1007/s10058-012-0134-6

Cite this article as:
Kıbrıs, Ö. Rev Econ Design (2012) 16: 269. doi:10.1007/s10058-012-0134-6

Abstract

We analyze the implications of Nash’s (Econometrica 18:155–162, 1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (J Econ Theory 16:247–251, 1977), we introduce a weaker independence of irrelevant alternatives (IIA) axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley–Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker IIA axiom. We also analyze the implications of other independence axioms.

Keywords

Bargaining Shapley–Shubik rule Ordinal invariance Independence of irrelevant alternatives Brace 

JEL Classification 

C78 

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Faculty of Arts and Social SciencesSabancı UniversityIstanbulTurkey

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