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Nash demand game and the Kalai-Smorodinsky solution

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  • Anbarci, Nejat
  • Boyd III, John H.

Abstract

We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the Kalai-Smorodinsky solution always finishes on top, there is no possible general ranking among the remaining solution concepts considered; in fact, the rest of the solution concepts take their turns at the bottom at various bargaining problems, depending on the specifics of the bargaining setup.

Suggested Citation

  • Anbarci, Nejat & Boyd III, John H., 2008. "Nash demand game and the Kalai-Smorodinsky solution," Working Papers eco_2008_11, Deakin University, Department of Economics.
  • Handle: RePEc:dkn:econwp:eco_2008_11
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    File URL: http://dx.doi.org/10.1016/j.geb.2010.07.009
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    References listed on IDEAS

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    1. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Bigelow, John Payne & Anbarci, Nejat, 1993. "Non-dictatorial, Pareto-monotonic, cooperative bargaining : An impossibility theorem," European Journal of Political Economy, Elsevier, vol. 9(4), pages 551-558, November.
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    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Nejat Anbarci, 1993. "Noncooperative Foundations of the Area Monotonic Solution," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 245-258.
    7. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-1186, September.
    8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    9. Ken Binmore, 1998. "Game Theory and the Social Contract - Vol. 2: Just Playing," MIT Press Books, The MIT Press, edition 1, volume 2, number 0262024446, May.
    10. Miyagawa, Eiichi, 2002. "Subgame-perfect implementation of bargaining solutions," Games and Economic Behavior, Elsevier, vol. 41(2), pages 292-308, November.
    11. Yusuke Samejima, 2005. "A Note on Implementation of Bargaining Solutions," Theory and Decision, Springer, vol. 59(3), pages 175-191, November.
    12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    13. Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-682, August.
    14. 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.
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    Cited by:

    1. Spinnewijn, Johannes & Spinnewyn, Frans, 2015. "Revising claims and resisting ultimatums in bargaining problems," LSE Research Online Documents on Economics 66197, London School of Economics and Political Science, LSE Library.
    2. Anbarci, Nejat & Feltovich, Nick, 2012. "Bargaining with random implementation: An experimental study," Games and Economic Behavior, Elsevier, vol. 76(2), pages 495-514.
    3. 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.
    4. Kang Rong, 2015. "Bargaining with split-the-difference arbitration," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 441-455, September.

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