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The Rights-Egalitarian Solution for NTU Sharing Problems

Author

Listed:
  • Carmen Herrero

    () (Universidad de Alicante & Ivie)

  • Antonio Villar

    () (Department of Economics, Universidad Pablo de Olavide & Ivie)

Abstract

The purpose of this paper is to extend the Rights Egalitarian solution (Herrero, Maschler & Villar, 1999) to the context of non-transferable utility sharing problems. Such an extension is not unique. Depending on the kind of properties we want to preserve we obtain two different generalizations. One is the "proportional solution", that corresponds to the Kalai-Smorodinsky solution for surplus sharing problems and the solution in Herrero (1998) for rationing problems. The other is the "Nash solution” that corresponds to the standard Nash bargaining solution for surplus sharing problems and the Nash rationing solution (Mariotti & Villar (2005) for the case of rationing problems.

Suggested Citation

  • Carmen Herrero & Antonio Villar, 2009. "The Rights-Egalitarian Solution for NTU Sharing Problems," Working Papers 09.01, Universidad Pablo de Olavide, Department of Economics.
  • Handle: RePEc:pab:wpaper:09.01
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    References listed on IDEAS

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    1. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
    8. Marco Mariotti & Antonio Villar, 2005. "The Nash rationing problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 367-377, September.
    9. Sergiu Hart, 2004. "A comparison of non-transferable utility values," Theory and Decision, Springer, vol. 56(1), pages 35-46, April.
    10. Sergiu Hart, 2005. "An axiomatization of the consistent non-transferable utility value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 355-366, September.
    11. Carmen Herrero, 1997. "Endogenous reference points and the adjusted proportional solution for bargaining problems with claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 113-119.
    12. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    13. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    14. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
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    Cited by:

    1. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    2. Andrea Gallice, 2016. "Bankruptcy Problems with Reference-Dependent Preferences," Working papers 038, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    3. Balakrishnan, P.V. (Sundar) & Gómez, Juan Camilo & Vohra, Rakesh V., 2011. "The Tempered Aspirations solution for bargaining problems with a reference point," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 144-150.

    More about this item

    Keywords

    Sharing problems; rights egalitarian solution; NTU problems.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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