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Nash bargaining in ordinal environments

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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. Copyright Springer-Verlag 2012

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Bibliographic Info

Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 16 (2012)
Issue (Month): 4 (December)
Pages: 269-282

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Handle: RePEc:spr:reecde:v:16:y:2012:i:4:p:269-282

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Related research

Keywords: Bargaining; Shapley–Shubik rule; Ordinal invariance; Independence of irrelevant alternatives; Brace; C78;

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  1. 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.
  2. 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.
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  4. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
  5. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  6. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  7. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
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Cited by:
  1. Vidal-Puga, Juan, 2013. "A non-cooperative approach to the ordinal Shapley rule," MPRA Paper 43790, University Library of Munich, Germany.

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