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Nucleoli as maximizers of collective satisfaction functions

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  • Sudhölter, Peter

    (Center for Mathematical Economics, Bielefeld University)

  • Peleg, Bezalel

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Two preimputations of a given TU game can be compared via the Lorenz order applied to the vectors of satisfactions. One preimputation is `socially more desirable' than the other, if its corresponding vector of satisfactions Lorenz dominates the satisfaction vector with respect to the second preimputation. It is shown that the prenucleolus, the anti-prenucleolus, and the modified nucleolus are maximal in this Lorenz order. Here the modified nucleolus is the unique preimputation which lexicographically minimizes the envies between the coalitions, i.e. the differences of excesses. Recently SudhÃlter developed this solution concept. Properties of the set of all undominated preimputations, the maximal satisfaction solution, are discussed. A function on the set of preimputations is called collective satisfaction function if it respects the Lorenz order. We prove that both classical nucleoli are unique minimizers of certain `weighted Gini inequality indices', which are derived from some collective satisfaction functions. For the (pre)nucleolus the function proposed by Kohlberg, who characterized the nucleolus as a solution of a single minimization problem, can be chosen. Finally, a collective satisfaction function is defined such that the modified nucleolus is its unique maximizer.
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Suggested Citation

  • Sudhölter, Peter & Peleg, Bezalel, 2017. "Nucleoli as maximizers of collective satisfaction functions," Center for Mathematical Economics Working Papers 262, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:262
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    Cited by:

    1. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    2. Natalia I. Naumova, 2022. "Some solutions for generalized games with restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 1077-1093, November.
    3. Arin Aguirre, Francisco Javier, 2003. "Egalitarian distributions in coalitional models: The Lorenz criterion," IKERLANAK 6503, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    4. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.

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