IDEAS home Printed from https://ideas.repec.org/p/ico/wpaper/67.html
   My bibliography  Save this paper

Stability, Fairness and Random Walks in the Bargaining Problem

Author

Listed:
  • Jakob Kapeller

    (Institute for Comprehensive Analysis of the Economy, Johannes Kepler University Linz, Austria)

  • Stefan Steinerberger

    (Department of Mathematics, Yale University, US)

Abstract

We study the classical bargaining problem and its two canonical solutions, (Nash and Kalai-Smorodinsky), from a novel point of view: we ask for stability of the solution if both players are able distort the underlying bargaining process by reference to a third party (e.g. a court). By exploring the simplest case, where decisions of the third party are made randomly we obtain a stable solution, where players do not have any incentive to refer to such a third party. While neither the Nash nor the Kalai-Smorodinsky solution are able to ensure stability in case reference to a third party is possible, we found that the Kalai-Smorodinsky solution seems to always dominate the stable allocation which constitutes novel support in favor of the latter.

Suggested Citation

  • Jakob Kapeller & Stefan Steinerberger, 2017. "Stability, Fairness and Random Walks in the Bargaining Problem," ICAE Working Papers 67, Johannes Kepler University, Institute for Comprehensive Analysis of the Economy.
    • Handle: RePEc:ico:wpaper:67
    as

    Download full text from publisher

    File URL: https://www.jku.at/fileadmin/gruppen/108/ICAE_Working_Papers/wp67.pdf
    File Function: First version, 2017
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    3. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
    4. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    5. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 709-724.
    6. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    7. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. William Thomson (ed.), 2010. "Bargaining and the Theory of Cooperative Games: John Nash and Beyond," Books, Edward Elgar Publishing, number 13317.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barry Nalebuff, 2021. "A Perspective-Invariant Approach to Nash Bargaining," Management Science, INFORMS, vol. 67(1), pages 577-593, January.
    2. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    3. Younghwan In, 2008. "On the relevance of alternatives in bargaining: generalized average pay-off solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 251-264, June.
    4. Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    5. Anbarci, Nejat & Boyd III, John H., 2011. "Nash demand game and the Kalai-Smorodinsky solution," Games and Economic Behavior, Elsevier, vol. 71(1), pages 14-22, January.
    6. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    7. l'Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2013. "Does bargaining matter in the small firms matching model?," Labour Economics, Elsevier, vol. 21(C), pages 42-58.
    8. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    9. M. Voorneveld & A. Nouweland & R. McLean, 2011. "Axiomatizations of the Euclidean compromise solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 427-448, August.
    10. Johannes Spinnewijn & Frans Spinnewyn, 2015. "Revising claims and resisting ultimatums in bargaining problems," Review of Economic Design, Springer;Society for Economic Design, vol. 19(2), pages 91-116, June.
    11. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Spulber, Daniel F., 2016. "Patent licensing and bargaining with innovative complements and substitutes," Research in Economics, Elsevier, vol. 70(4), pages 693-713.
    13. Nejat Anbarci, 1998. "Simple Characterizations of the Nash and Kalai/smorodinsky Solutions," Theory and Decision, Springer, vol. 45(3), pages 255-261, December.
    14. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.
    15. Bossert, Walter & Peters, Hans, 2001. "Minimax Regret and Efficient Bargaining under Uncertainty," Games and Economic Behavior, Elsevier, vol. 34(1), pages 1-10, January.
    16. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    17. Takeuchi, Ai & Veszteg, Róbert F. & Kamijo, Yoshio & Funaki, Yukihiko, 2022. "Bargaining over a jointly produced pie: The effect of the production function on bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 134(C), pages 169-198.
    18. Naeve-Steinweg, Elisabeth, 2002. "Mechanisms supporting the Kalai-Smorodinsky solution," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 25-36, September.
    19. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    20. Yakov Babichenko & Leonard J. Schulman, 2015. "Pareto Efficient Nash Implementation Via Approval Voting," Papers 1502.05238, arXiv.org, revised Mar 2017.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ico:wpaper:67. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Teresa Griesebner (email available below). General contact details of provider: https://edirc.repec.org/data/igjkuat.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.