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Robustness of Intermediate Agreements and Bargaining Solutions


  • Nejat Anbarci


  • Ching-jen Sun



Most real-life bargaining is resolved gradually; two parties reach intermediate agreements without knowing the whole range of possibilities. These intermediate agreements serve as disagreement points in subsequent rounds. Cooperative bargaining solutions ignore these dynamics and can therefore yield accurate predictions only if they are robust to its specification. We identify robustness criteria which are satisfied by four of the best-known bargaining solutions, the Nash, Kalai-Smorodinsky, Proportional and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide the first characterization of the Discrete Raiffa solution and novel axiomatizations of the other three solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories.

Suggested Citation

  • Nejat Anbarci & Ching-jen Sun, 2009. "Robustness of Intermediate Agreements and Bargaining Solutions," Economics Series 2009_14, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  • Handle: RePEc:dkn:econwp:eco_2009_14

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    References listed on IDEAS

    1. Trockel, Walter, 2011. "An axiomatization of the sequential Raiffa solution," Center for Mathematical Economics Working Papers 425, Center for Mathematical Economics, Bielefeld University.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. 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.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. 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.
    6. Chun, Youngsub, 1988. "Nash solution and timing of bargaining," Economics Letters, Elsevier, vol. 28(1), pages 27-31.
    7. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-959, July.
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    11. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    12. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881, December.
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    14. 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.
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    Cited by:

    1. 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.
    2. Trockel, Walter, 2014. "Robustness of intermediate agreements for the discrete Raiffa solution," Games and Economic Behavior, Elsevier, pages 32-36.

    More about this item


    Nash’s bargaining problem; robustness; intermediate agreements; the Discrete Raiffa solution; the Nash solution; the Kalai-Smorodinsky solution; Proportional solutions.;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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