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Generalized Maximin Solutions in Multicriteria Bargaining

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  • M. Hinojosa
  • A. Mármol
  • L. Monroy

Abstract

In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions. We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish some properties of these solutions and characterize them as solutions of multicriteria problems. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • M. Hinojosa & A. Mármol & L. Monroy, 2005. "Generalized Maximin Solutions in Multicriteria Bargaining," Annals of Operations Research, Springer, vol. 137(1), pages 243-255, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:243-255:10.1007/s10479-005-2259-2
    DOI: 10.1007/s10479-005-2259-2
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Pekka Korhonen & Herbert Moskowitz & Jyrki Wallenius & Stanley Zionts, 1986. "An interactive approach to multiple criteria optimization with multiple decision‐makers," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 589-602, November.
    3. Marmol, Amparo M. & Puerto, Justo & Fernandez, Francisco R., 2002. "Sequential incorporation of imprecise information in multiple criteria decision processes," European Journal of Operational Research, Elsevier, vol. 137(1), pages 123-133, February.
    4. Clara Ponsati & Joel Watson, 1998. "Multiple-Issue Bargaining and Axiomatic Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(4), pages 501-524.
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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. L. Monroy & V. Rubiales & A. M. Mármol, 2017. "The conservative Kalai–Smorodinsky solution for multiple scenario bargaining," Annals of Operations Research, Springer, vol. 251(1), pages 285-299, April.

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