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Nash demand game and the Kalai-Smorodinsky solution


  • Anbarci, Nejat
  • Boyd III, John H.


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," Economics Series eco_2008_11, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  • Handle: RePEc:dkn:econwp:eco_2008_11

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    References listed on IDEAS

    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. 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.
    3. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
    4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    5. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-682, August.
    8. Miyagawa, Eiichi, 2002. "Subgame-perfect implementation of bargaining solutions," Games and Economic Behavior, Elsevier, vol. 41(2), pages 292-308, November.
    9. 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.
    10. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    11. 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.
    12. Nejat Anbarci, 1993. "Noncooperative Foundations of the Area Monotonic Solution," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 245-258.
    13. 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, July.
    14. Yusuke Samejima, 2005. "A Note on Implementation of Bargaining Solutions," Theory and Decision, Springer, vol. 59(3), pages 175-191, November.
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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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