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What if Achilles and the tortoise were to bargain? An argument against interim agreements

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  • Samet, Dov

Abstract

Zeno's paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson's Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno's, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by \cite{ra}, and show that no agreement is reached along this path in finite time.

Suggested Citation

  • Samet, Dov, 2009. "What if Achilles and the tortoise were to bargain? An argument against interim agreements," MPRA Paper 23370, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:23370
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    File URL: https://mpra.ub.uni-muenchen.de/23370/1/MPRA_paper_23370.pdf
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    References listed on IDEAS

    as
    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. O'Neill, Barry & Samet, Dov & Wiener, Zvi & Winter, Eyal, 2004. "Bargaining with an agenda," Games and Economic Behavior, Elsevier, vol. 48(1), pages 139-153, July.
    4. 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.
    5. 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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    2. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 603-622, August.

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    More about this item

    Keywords

    Zeno's paradox; bargaining problems; interim agreements; vNM utility;
    All these keywords.

    JEL classification:

    • D73 - Microeconomics - - Analysis of Collective Decision-Making - - - Bureaucracy; Administrative Processes in Public Organizations; Corruption
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • 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
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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