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The equity core and the Lorenz-maximal allocations in the equal division core

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  • Francesc Llerena
  • Cori Vilella

Abstract

In this note, we give a geometrical decomposition of the equity core as a finite union of polyhedrons. As a consequence, we characterize the non-emptiness of the equity core (Selten in Decision theory and social ethics: issues in social choice, Reidel, Dordrecht, 289–301, 1978 ) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta and Ray in Games Econ Behav 3:403–422, 1991 ). Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Francesc Llerena & Cori Vilella, 2015. "The equity core and the Lorenz-maximal allocations in the equal division core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 235-244, April.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:2:p:235-244
    DOI: 10.1007/s00186-015-0494-0
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    1. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 391-399, April.
    2. 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.
    3. Francesc Llerena & Cori Vilella, 2013. "An axiomatic characterization of the strong constrained egalitarian solution," Economics Bulletin, AccessEcon, vol. 33(2), pages 1438-1445.
    4. Dutta, Bhaskar & Ray, Debraj, 1991. "Constrained egalitarian allocations," Games and Economic Behavior, Elsevier, vol. 3(4), pages 403-422, November.
    5. Arin, Javier & Kuipers, Jeroen & Vermeulen, Dries, 2003. "Some characterizations of egalitarian solutions on classes of TU-games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 327-345, December.
    6. Carles Rafels & Cori Vilella, 2007. "Proportional share analysis," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 341-354, December.
    7. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 147-165.
    8. Francesc Llerena & Carles Rafels & Cori Vilella, 2008. "A simple procedure for computing strong constrained egalitarian allocations," Working Papers 327, Barcelona School of Economics.
    9. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    10. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
    11. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 565-580, December.
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    More about this item

    Keywords

    Cooperative game; Equity core; Equal division core ; Lorenz domination;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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