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Individual disagreement point concavity and the bargaining problem

Author

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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

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    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. Livne, Zvi A., 1988. "The bargaining problem with an uncertain conflict outcome," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 287-302, June.
    3. Adrian Van Deemen & Agnieszka Rusinowska (ed.), 2010. "Collective Decision Making," Theory and Decision Library C, Springer, number 978-3-642-02865-6, March.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. Chun, Youngsub & Thomson, William, 1990. "Nash solution and uncertain disagreement points," Games and Economic Behavior, Elsevier, vol. 2(3), pages 213-223, September.
    6. Adrian van Deemen & Agnieszka Rusinowska, 2010. "Collective Decision Making: Views from Social Choice and Game Theory," Post-Print hal-00514840, HAL.
    7. Chun, Youngsub & Thomson, William, 1990. "Egalitarian solutions and uncertain disagreement points," Economics Letters, Elsevier, vol. 33(1), pages 29-33, May.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. 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.
    10. 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.
    11. 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.
    12. McDonald, Ian M & Solow, Robert M, 1981. "Wage Bargaining and Employment," American Economic Review, American Economic Association, vol. 71(5), pages 896-908, December.
    13. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-959, July.
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    Cited by:

    1. Kensei Nakamura, 2024. "Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 629-642, June.

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