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An axiomatization of the sequential Raiffa solution

Author

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  • Trockel, Walter

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper provides four axioms that uniquely characterize the sequential Raiffa solution proposed by Raiffa (1951, 1953) for two-person bargaining games. Three of these axioms are standard and are shared by several popular bargaining solutions. They suffice to characterize these solutions on TU-bargaining games where they coincide. The fourth axiom is a weakening of Kalai's (1977) axiom of step-by-step negotiating and turns out to be sort of a dual condition to a weaker version of Nash's IIA-axiom that together with the three standard axioms suffices to characterize the Nash bargaining solution due to Nash (1950). A conclusion of this axiomatization is that in contrast to all other known bargaining solutions the sequential Raiffa solution does not represent just another kind of fairness or equity condition in addition to the three standard axioms but rather is determined by indefinite repeated application of the three standard axioms.

Suggested Citation

  • Trockel, Walter, 2011. "An axiomatization of the sequential Raiffa solution," Center for Mathematical Economics Working Papers 425, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:425
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    File URL: https://pub.uni-bielefeld.de/download/2316445/2319869
    File Function: First Version, 2009
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    Citations

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    Cited by:

    1. Ismail Saglam, 2014. "A Simple Axiomatization Of The Egalitarian Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-7.
    2. Eric Guerci & Sylvie Thoron, 2011. "Experimental comparison of compulsory and non compulsory arbitration mechanisms," Working Papers halshs-00584328, HAL.
    3. Emily Tanimura & Sylvie Thoron, 2016. "How Best to Disagree in Order to Agree?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-17, September.
    4. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    5. Trockel, Walter, 2014. "Robustness of intermediate agreements for the discrete Raiffa solution," Games and Economic Behavior, Elsevier, vol. 85(C), pages 32-36.
    6. Ismail Saglam, 2017. "Iterated Kalai–Smorodinsky–Nash compromise," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 335-349, November.
    7. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    8. Claus-Jochen Haake, 2009. "Dividing By Demanding: Object Division Through Market Procedures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 15-32.
    9. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    10. Walter Trockel, 2015. "Axiomatization of the discrete Raiffa solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 9-17, April.
    11. Haake, Claus-Jochen, 2016. "Dividing by Demanding: Object Division through Market Procedures," Center for Mathematical Economics Working Papers 359, Center for Mathematical Economics, Bielefeld University.
    12. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 603-622, August.

    More about this item

    Keywords

    Nash solution; Axiomatization; Raiffa solution; Bargaining games;
    All these keywords.

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