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

@article{GonzlezDaz2014UnderstandingTC,
  title={Understanding the coincidence of allocation rules: symmetry and orthogonality in TU-games},
  author={Julio Gonz{\'a}lez-D{\'i}az and Estela S{\'a}nchez-Rodr{\'i}guez},
  journal={International Journal of Game Theory},
  year={2014},
  volume={43},
  pages={821-843}
}
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… 
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