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Fairness, Efficiency, and the Nash Bargaining Solution

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Abstract

A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian solutions to a weighted Nash solution, is obtained. These results are related to a theorem of Shapley, which I generalize. For n>=3, there does not exist any n-person scale-invariant bargaining solution that balances fairness and efficiency.

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  • Rachmilevitch, Shiran, "undated". "Fairness, Efficiency, and the Nash Bargaining Solution," Working Papers WP2011/10, University of Haifa, Department of Economics.
    • Handle: RePEc:haf:huedwp:wp201110
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    References listed on IDEAS

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    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Nejat Anbarci, 1998. "Simple Characterizations of the Nash and Kalai/smorodinsky Solutions," Theory and Decision, Springer, vol. 45(3), pages 255-261, December.
    3. Yaari, Menahem E., 1981. "Rawls, edgeworth, shapley, nash: Theories of distributive justice re-examined," Journal of Economic Theory, Elsevier, vol. 24(1), pages 1-39, February.
    4. 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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    Cited by:

    1. Rachmilevitch, Shiran, "undated". "The Nash Bargaining Solution and Interpersonal Utility Comparisons," Working Papers WP2012/1, University of Haifa, Department of Economics.
    2. Wentao Yi & Zhongwei Feng & Chunqiao Tan & Yuzhong Yang, 2021. "Green Supply Chain Management with Nash Bargaining Loss-Averse Reference Dependence," Mathematics, MDPI, vol. 9(24), pages 1-26, December.

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    More about this item

    Keywords

    Bargaining; fairness; efficiency; Nash solution;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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