Nash bargaining in ordinal environments
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. Copyright Springer-Verlag 2012
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Volume (Year): 16 (2012)
Issue (Month): 4 (December)
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References listed on IDEAS
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- Kalai, Ehud, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
Econometric Society, vol. 45(7), pages 1623-30, October.
- Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Zvi Safra & Dov Samet, 2003.
"An ordinal solution to bargaining problems with many players,"
Game Theory and Information
- Safra, Zvi & Samet, Dov, 2004. "An ordinal solution to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 46(1), pages 129-142, January.
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- Samet, Dov & Safra, Zvi, 2005. "A family of ordinal solutions to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 50(1), pages 89-106, January.
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- Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
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