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Egalitarian solutions in the core

Author

Listed:
  • Javier Arin

    (Universidad Pais Vasco, Fundamentos Analisis Economico, Avenida Lehendakari Aguirre 83, 48015 Bilbao, Spain)

  • Elena Inarra

    (Universidad Pais Vasco, Fundamentos Analisis Economico, Avenida Lehendakari Aguirre 83, 48015 Bilbao, Spain)

Abstract

In this paper we define the Lorenz stable set, a subset of the core consisting of the allocations that are not Lorenz dominated by any other allocation of the core. We introduce the leximin stable allocation, which is derived from the application of the Rawlsian criterion on the core. We also define and axiomatize the egalitarian core, a set of core allocations for which no transfer from a rich player to a poor player is possible without violating the core restrictions. We find an inclusive relation of the leximin stable allocation and of the Lorenz stable set into the egalitarian core.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:187-193
    Note: Received: October 1999/Final version: July 2001
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    Citations

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    Cited by:

    1. 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.
    2. Laurent Lamy, 2009. "Ascending auctions: some impossibility results and their resolutions with final price discounts," PSE Working Papers halshs-00575076, HAL.
    3. Arin Aguirre, Francisco Javier, 2003. "Egalitarian distributions in coalitional models: The Lorenz criterion," IKERLANAK 2003-02, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    4. J. Arin & E. Inarra & P. Luquin, 2009. "A noncooperative view on two airport cost sharing rules," Review of Economic Design, Springer;Society for Economic Design, vol. 13(4), pages 361-376, December.
    5. Francesc Llerena & Carles Rafels & Cori Vilella, 2008. "A simple procedure for computing strong constrained egalitarian allocations," Working Papers 327, Barcelona Graduate School of Economics.
    6. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    7. 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.
    8. Laurent Lamy, 2009. "Ascending auctions: some impossibility results and their resolutions with final price discounts," Working Papers halshs-00575076, HAL.
    9. Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, vol. 78(1), pages 141-151, January.
    10. Arin Aguirre, Francisco Javier & Feltkamp, Vincent, 2005. "Implementing with veto players: a simple non cooperative game," IKERLANAK 2005-17, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    11. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 313-325, May.
    12. Francesc Llerena & Llúcia Mauri, 2015. "On the Lorenz-maximal allocations in the imputation set," Economics Bulletin, AccessEcon, vol. 35(4), pages 2475-2481.
    13. repec:eee:matsoc:v:89:y:2017:i:c:p:92-99 is not listed on IDEAS
    14. Arin Aguirre, Francisco Javier & Iñarra García, María Elena & Luquin, Paloma, 2006. "A noncooperative view on two consistent aiport cost sharing rules," IKERLANAK 2006-23, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    15. Arin Aguirre, Francisco Javier & Iñarra García, María Elena & Luquin, Paloma, 2006. "A noncooperative view on two consistent aiport cost sharing rules," IKERLANAK 2006-23, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    16. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    17. Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1053-1069, November.
    18. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Discussion Paper 2004-110, Tilburg University, Center for Economic Research.
    19. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2014. "On reduced games and the lexmax solution," Working Papers 2072/237591, Universitat Rovira i Virgili, Department of Economics.
    20. repec:eee:gamebe:v:106:y:2017:i:c:p:179-187 is not listed on IDEAS
    21. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2016. "The Procedural Egalitarian Solution," Discussion Paper 2016-041, Tilburg University, Center for Economic Research.
    22. Sánchez-Soriano, J. & Brânzei, R. & Llorca, N. & Tijs, S.H., 2010. "A Technical Note on Lorenz Dominance in Cooperative Games," Discussion Paper 2010-101, Tilburg University, Center for Economic Research.
    23. Arin, J. & Feltkamp, V., 2007. "Coalitional games with veto players: Consistency, monotonicity and Nash outcomes," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 855-870, September.
    24. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Discussion Paper 2007-55, Tilburg University, Center for Economic Research.

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