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A generalization of the Egalitarian and the Kalai–Smorodinsky bargaining solutions

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Listed:
  • Dominik Karos

    (Maastricht University)

  • Nozomu Muto

    (Yokohama National University)

  • Shiran Rachmilevitch

    (University of Haifa)

Abstract

We characterize the class of weakly efficient n-person bargaining solutions that solely depend on the ratios of the players’ ideal payoffs. In the case of at least three players the ratio between the solution payoffs of any two players is a power of the ratio between their ideal payoffs. As special cases this class contains the Egalitarian and the Kalai–Smorodinsky bargaining solutions, which can be pinned down by imposing additional axioms.

Suggested Citation

  • Dominik Karos & Nozomu Muto & Shiran Rachmilevitch, 2018. "A generalization of the Egalitarian and the Kalai–Smorodinsky bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1169-1182, November.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:4:d:10.1007_s00182-018-0611-4
    DOI: 10.1007/s00182-018-0611-4
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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. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    3. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
    4. Lensberg, T. & Thomson, W., 1988. "Characterizing The Nash Bargaining Solution Without Pareto-Optimality," RCER Working Papers 136, University of Rochester - Center for Economic Research (RCER).
    5. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    6. 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.
    7. Driesen, Bram, 2016. "Truncated Leximin solutions," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 79-87.
    8. van Damme, E.E.C. & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Other publications TiSEM 4bd5eb9e-328a-45a0-aa0a-e, Tilburg University, School of Economics and Management.
    9. 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.
    10. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    12. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    13. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    14. 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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