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Nash bargaining theory when the number of alternatives can be finite


  • Marco Mariotti

    (Department of Economics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, UK)


Nash (1950) considered a domain of convex bargaining problems. We analyse domains including, or even consisting of, finite problems and provide various characterisations of the Nash Bargaining Solution (NBS). In particular, we extend Kaneko's (1980) results.

Suggested Citation

  • Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 413-421.
  • Handle: RePEc:spr:sochwe:v:15:y:1998:i:3:p:413-421
    Note: Received: 12 July 1996 / Accepted: 6 February 1997

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    References listed on IDEAS

    1. Dan S. Felsenthal & MoshÚ Machover, 2004. "Qualified Majority Voting Explained," Homo Oeconomicus, Institute of SocioEconomics, vol. 21, pages 573-576.
    2. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    3. Algaba, E. & Bilbao, J. M. & Fernandez Garcia, J. R. & Lopez, J. J., 2003. "Computing power indices in weighted multiple majority games," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 63-80, August.
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    5. Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006. "L S Penrose's limit theorem: Tests by simulation," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 90-106, January.
    6. Thomas Stratmann & Martin Baur, 2002. "Plurality Rule, Proportional Representation, and the German Bundestag: How Incentives to Pork-Barrel Differ Across Electoral Systems," CESifo Working Paper Series 650, CESifo Group Munich.
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    Cited by:

    1. Fabio Galeotti, 2017. "The Attraction and Compromise Effects in Bargaining: Experimental Evidence," Post-Print halshs-01657317, HAL.
    2. Xu, Yongsheng & Yoshihara, Naoki, 2013. "Rationality and solutions to nonconvex bargaining problems: Rationalizability and Nash solutions," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 66-70.
    3. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    4. Attanasi, Giuseppe & Corazzini, Luca & Passarelli, Francesco, 2017. "Voting as a lottery," Journal of Public Economics, Elsevier, vol. 146(C), pages 129-137.
    5. Cheng-Zhong Qin & Shuzhong Shi & Guofu Tan, 2015. "Nash bargaining for log-convex problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 413-440, April.
    6. Zambrano, Eduardo, 2016. "‘Vintage’ Nash bargaining without convexity," Economics Letters, Elsevier, vol. 141(C), pages 32-34.
    7. Lombardi, Michele & Yoshihara, Naoki, 2010. "Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims," Economics Letters, Elsevier, vol. 108(2), pages 229-232, August.
    8. Xu, Yongsheng & Yoshihara, Naoki, 2011. "Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems," CCES Discussion Paper Series 42, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    9. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    10. Vincenzo Denicolò & Marco Mariotti, 2000. "Nash Bargaining Theory, Nonconvex Problems and Social Welfare Orderings," Theory and Decision, Springer, vol. 48(4), pages 351-358, June.
    11. Marco Mariotii, 1996. "Fair bargains: distributive justice and Nash Bargaining Theory," Game Theory and Information 9611003, EconWPA, revised 06 Dec 1996.
    12. John Conley & Simon Wilkie, 2012. "The ordinal egalitarian bargaining solution for finite choice sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 23-42, January.

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