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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23370.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:23370

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Keywords: Zeno's paradox; bargaining problems; interim agreements; vNM utility;

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References

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  1. Damme, E.E.C. van & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154419, Tilburg University.
  2. 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.
  3. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
  4. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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Cited by:
  1. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer, vol. 41(3), pages 603-622, August.

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