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Population-Monotonicity of the Nucleolus on a Class of Public Good Problems

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  • Sonmez, Tayfun O.

Abstract

Sprumont (1990) shows that the Shapley value (Shapley 1957) is population-monotonic (Thomson 1983) on the class of convex games (Shapley 1971). In this paper we study the population-monotonicity of the nucleolus (Schmeidler 1969). We show that the nucleolus is not population-monotonic on the class of convex games. Our main result is that the nucleolus is population-monotonic on a class of public good problems which is formalized in Litilechild and Owen (1973) under the name of airport games. We also provide a recursive formula for the nucleolus of the airport game.

Suggested Citation

  • Sonmez, Tayfun O., 2014. "Population-Monotonicity of the Nucleolus on a Class of Public Good Problems," MPRA Paper 58248, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:58248
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    References listed on IDEAS

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    1. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    3. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
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    Cited by:

    1. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
    2. Yan-An Hwang & Chun-Hsien Yeh, 2012. "A characterization of the nucleolus without homogeneity in airport problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 355-364, February.

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    JEL classification:

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

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