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On the set of Lorenz-maximal imputations in the core of a balanced game

Author

Listed:
  • Jens Leth Hougaard

    () (Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K., Denmark.)

  • Lars Thorlund-Petersen

    (Copenhagen Business School, Department of Operations Management, Solbjerg Pl. 3, 2000 Frederiskberg, DENMARK)

  • Bezalel Peleg

    (Hebrew University Jerusalem, Center Rationality, Interaction, Decision Theory, Givat-Ram, Feldman Building, 91 904 Jerusalem, ISRAEL)

Abstract

This paper considers the set of Lorenz-maximal imputations in the core of a balanced cooperative game as a solution concept. It is shown that the Lorenz-solution concept satisfies a number of suitable properties such as desirability, continuity and the reduced game property. Moreover, the paper consideres alternative characterizations where it is shown that Lorenz-fairness is tantamount to the existence of an additive, strictly increasing and concave social welfare function. Finally the paper also provides axiomatic characterizations as well as two examples of application.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:147-165 Note: Received: February 1999/Final version: June 2001
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    1. repec:cup:apsrev:v:84:y:1990:i:01:p:237-241_19 is not listed on IDEAS
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    Cited by:

    1. repec:eee:matsoc:v:89:y:2017:i:c:p:92-99 is not listed on IDEAS
    2. Jens Leth Hougaard & Aleksandrs Smilgins, 2014. "Risk Capital Allocation: The Lorenz Set," MSAP Working Paper Series 03_2014, University of Copenhagen, Department of Food and Resource Economics.
    3. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, pages 763-774.
    4. 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.
    5. 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), pages 235-244.
    6. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, pages 313-325.
    7. 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.
    8. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    9. Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Risk capital allocation with autonomous subunits: The Lorenz set," Insurance: Mathematics and Economics, Elsevier, pages 151-157.
    10. Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, pages 1053-1069.
    11. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2016. "On the existence of the Dutta-Ray’s egalitarian solution," Working Papers 2072/266573, Universitat Rovira i Virgili, Department of Economics.
    12. Elena B.Yanovskaya, 2014. "Self-Covariant Solutions To Cooperative Games With Transferable Utilities," HSE Working papers WP BRP 85/EC/2014, National Research University Higher School of Economics.
    13. Francesc Llerena & Carles Rafels & Cori Vilella, 2008. "A simple procedure for computing strong constrained egalitarian allocations," Working Papers 327, Barcelona Graduate School of Economics.
    14. 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.
    15. Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, pages 141-151.
    16. 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.
    17. 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.
    18. Francesc Llerena & Cori Vilella, 2013. "An axiomatic characterization of the strong constrained egalitarian solution," Economics Bulletin, AccessEcon, vol. 33(2), pages 1438-1445.
    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. 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.
    21. Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, pages 141-151.
    22. 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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