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Reconciling Consistency and Continuity: A Bounded-Population Characterization of the Nash Bargaining Solution

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  • William Thomson

    (University of Rochester)

Abstract

This paper explores the robustness of a characterization of the Nash bargaining solution in a variable-population framework in which the population of players is bounded (Lensberg in J Econ Theory 45:330–341, 1988). A central axiom in this characterization is “consistency”, which says that the solution outcome of any problem should always be “confirmed” by the solution in the “reduced problem” that results after some players have left with their assigned payoffs. Another axiom in this characterization is the standard requirement of Hausdorff continuity. We advocate a weaker version of continuity, a version that is a better conceptual fit with consistency that Hausdorff-continuity, and show that the Nash solution still emerges as the only one to satisfy all of the axioms.

Suggested Citation

  • William Thomson, 2020. "Reconciling Consistency and Continuity: A Bounded-Population Characterization of the Nash Bargaining Solution," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 43-57, November.
    • Handle: RePEc:spr:homoec:v:37:y:2020:i:1:d:10.1007_s41412-020-00103-y
    DOI: 10.1007/s41412-020-00103-y
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    References listed on IDEAS

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    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    3. Lensberg, T. & Thomson, W., 1988. "Characterizing The Nash Bargaining Solution Without Pareto-Optimality," RCER Working Papers 136, University of Rochester - Center for Economic Research (RCER).
    4. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    5. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    8. Salonen, Hannu, 1998. "Egalitarian solutions for n-person bargaining games," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 291-306, May.
    9. Salonen, Hannu, 1996. "Continuity Properties of Bargaining Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(4), pages 411-425.
    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.
    11. William Thomson (ed.), 2010. "Bargaining and the Theory of Cooperative Games: John Nash and Beyond," Books, Edward Elgar Publishing, number 13317.
    12. Thomson, William, 1984. "Monotonicity, stability and egalitarianism," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 15-28, August.
    13. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
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    Cited by:

    1. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.

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    More about this item

    Keywords

    Bargaining theory; Consistency; Continuity; Nash solution;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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