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Extension of the Perles-Maschler Solution to N-Person Bargaining Games


  • Calvo, Emilio
  • Gutierrez, Esther


The superadditive solution for 2-person Nash bargaining games was axiomatically defined in Perles/Maschler (1981). In Perles (1982) it was shown that the axioms are incompatible even for 3-person bargaining games. In this paper we offer a generalization method of this solution concept for n-person games. In this method, the Kalai-Smorodinsky solution (1975) is revealed as the rule followed to determine the movements along the path of intermediate agreements.

Suggested Citation

  • Calvo, Emilio & Gutierrez, Esther, 1994. "Extension of the Perles-Maschler Solution to N-Person Bargaining Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 325-346.
  • Handle: RePEc:spr:jogath:v:23:y:1994:i:4:p:325-46

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    References listed on IDEAS

    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-682, August.
    4. Thomson, William, 1981. "A class of solutions to bargaining problems," Journal of Economic Theory, Elsevier, vol. 25(3), pages 431-441, December.
    5. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
    6. 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.
    7. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    8. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
    9. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
    10. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    11. Tijs, S.H. & Peters, H., 1985. "Risk sensitivity and related properties for bargaining solutions," Other publications TiSEM 9715c0e3-8f88-482e-9a95-f, Tilburg University, School of Economics and Management.
    12. Younghwan In, 2002. "On the Relevance of Alternatives in Bargaining: Average Alternative Solutions," Departmental Working Papers wp0214, National University of Singapore, Department of Economics.
    13. Nejat Anbarci, 1993. "Noncooperative Foundations of the Area Monotonic Solution," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 245-258.
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    Cited by:

    1. Feimin Zhong & Jinxing Xie & Xiaobo Zhao, 2014. "The price of fairness with the extended Perles–Maschler solution," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 193-212, October.
    2. Ervig, U. & Haake, C.-J., 2005. "Trading bargaining weights," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 983-993, December.
    3. Rosenmüller, Joachim, 2011. "A value for cephoidal NTU-games," Center for Mathematical Economics Working Papers 388, Center for Mathematical Economics, Bielefeld University.
    4. repec:ebl:ecbull:v:3:y:2004:i:35:p:1-8 is not listed on IDEAS
    5. Ervig,U. & Haake,C., 2003. "Trading bargaining weights," Center for Mathematical Economics Working Papers 350, Center for Mathematical Economics, Bielefeld University.
    6. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.

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