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Two simple characterizations of the Nash bargaining solution

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  • Osamu Mori

    (Jobu University)

Abstract

We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom (Rachmilevitch in Theory Decis 80:427–442, 2016) and egalitarian Pareto optimality. We then demonstrate that the Nash solution is characterized by symmetry, scale invariance, strong undominatedness by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality.

Suggested Citation

  • Osamu Mori, 2018. "Two simple characterizations of the Nash bargaining solution," Theory and Decision, Springer, vol. 85(2), pages 225-232, August.
    • Handle: RePEc:kap:theord:v:85:y:2018:i:2:d:10.1007_s11238-017-9624-x
    DOI: 10.1007/s11238-017-9624-x
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    References listed on IDEAS

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    1. Vartiainen, Hannu, 2007. "Collective choice with endogenous reference outcome," Games and Economic Behavior, Elsevier, vol. 58(1), pages 172-180, January.
    2. Shiran Rachmilevitch, 2016. "Egalitarian–utilitarian bounds in Nash’s bargaining problem," Theory and Decision, Springer, vol. 80(3), pages 427-442, March.
    3. Nejat Anbarci & Ching-jen Sun, 2011. "Weakest collective rationality and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 425-429, September.
    4. Alvin E. Roth, 1977. "Individual Rationality and Nash's Solution to the Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 64-65, February.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Nejat Anbarci, 1998. "Simple Characterizations of the Nash and Kalai/smorodinsky Solutions," Theory and Decision, Springer, vol. 45(3), pages 255-261, December.
    8. Geoffroy Clippel, 2007. "An axiomatization of the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 201-210, September.
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    Cited by:

    1. NAKAMURA, Kensei, 2023. "Characterizing the Nash bargaining solution with continuity and almost no individual rationality," Discussion Papers 2023-02, Graduate School of Economics, Hitotsubashi University.
    2. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    3. Shiran Rachmilevitch, 2021. "No individual priorities and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 855-863, May.

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