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Individual disagreement point concavity and the bargaining problem

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  • Walter Bossert
  • Hans Peters

Abstract

In this study, we provide a characterization of the class of proportional bargaining solutions introduced by Kalai. Our result differs from earlier axiomatizations in that we use a property that we label individual disagreement point concavity. This property is a weakening of disagreement point concavity used by Chun and Thomson. An application illustrates the potential usefulness of our new property in a strategic setting.

Suggested Citation

  • Walter Bossert & Hans Peters, 2022. "Individual disagreement point concavity and the bargaining problem," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 6-15, March.
    • Handle: RePEc:bla:ijethy:v:18:y:2022:i:1:p:6-15
    DOI: 10.1111/ijet.12304
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    References listed on IDEAS

    as
    1. 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.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    4. Livne, Zvi A., 1988. "The bargaining problem with an uncertain conflict outcome," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 287-302, June.
    5. Adrian Van Deemen & Agnieszka Rusinowska (ed.), 2010. "Collective Decision Making," Theory and Decision Library C, Springer, number 978-3-642-02865-6, March.
    6. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    7. Chun, Youngsub & Thomson, William, 1990. "Nash solution and uncertain disagreement points," Games and Economic Behavior, Elsevier, vol. 2(3), pages 213-223, September.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    9. Adrian van Deemen & Agnieszka Rusinowska, 2010. "Collective Decision Making: Views from Social Choice and Game Theory," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514840, HAL.
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    12. Chun, Youngsub & Thomson, William, 1990. "Egalitarian solutions and uncertain disagreement points," Economics Letters, Elsevier, vol. 33(1), pages 29-33, May.
    13. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    14. Hans Peters & Walter Bossert, 2002. "Efficient solutions to bargaining problems with uncertain disagreement points," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 489-502.
    15. Zvi A. Livne, 1989. "On the Status Quo Sets Induced by the Raiffa Solution to the Two-Person Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 688-692, November.
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