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Understanding the coincidence of allocation rules: symmetry and orthogonality in TU-games

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  • Julio González-Díaz

  • Estela Sánchez-Rodríguez

Abstract

The main goal of this paper is to understand the reasons driving the coincidence of different allocation rules for different classes of games. We define a new symmetry property, reverse symmetry, and study its geometric and game theoretic implications. In particular, we show that most classic allocation rules satisfy it. Then, we introduce and study a notion of orthogonality between TU-games, which allows to establish a restricted additivity property for the nucleolus. Also, in our analysis we identify different classes of games for which all allocation rules satisfying some sets of basic properties coincide. These properties are satisfied, among others, by the Shapley value and the nucleolus. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Julio González-Díaz & Estela Sánchez-Rodríguez, 2014. "Understanding the coincidence of allocation rules: symmetry and orthogonality in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 821-843, November.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:821-843
    DOI: 10.1007/s00182-013-0406-6
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    References listed on IDEAS

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    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
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    7. Julio González-Díaz & Estela Sánchez-Rodríguez, 2007. "A natural selection from the core of a TU game: the core-center," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 27-46, September.
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    JEL classification:

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

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