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An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise

Author

Listed:
  • Saglam, Ismail
Abstract
In this paper, we offer for two-person games an alternative characterization of Iterated Kalai-Smorodinsky-Nash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$-person games. We present an axiom called Gamma-Decomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by Gamma-Decomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry.

Suggested Citation

  • Saglam, Ismail, 2016. "An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise," MPRA Paper 73564, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:73564
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    References listed on IDEAS

    as
    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, January.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    3. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, December.
    4. Rachmilevitch, Shiran, "undated". "Gradual Negotiations and Proportional Solutions," Working Papers WP2011/8, University of Haifa, Department of Economics.
    5. 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.
    6. Trockel, Walter, 2014. "Robustness of intermediate agreements for the discrete Raiffa solution," Games and Economic Behavior, Elsevier, vol. 85(C), pages 32-36.
    7. Salonen, Hannu, 1988. "Decomposable solutions for N -- person bargaining games," European Journal of Political Economy, Elsevier, vol. 4(3), pages 333-347.
    8. 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.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative bargaining; Kalai-Smorodinsky solution; Nash solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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