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On the coincidence property

Author

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  • Chang, Chih
  • Tseng, Ying-Chih

Abstract

The collection of the coalitions b is balanced if the Shapley value of the simple game [chi]b is 0. This observation makes us able to derive a class of simple games with the coincidence property, that is, the Shapley value and the nucleolus coincide. And then we use such a class of simple games as generators to construct coincidence regions, convex cones consisting of games with the coincidence property. We will first propose the SP region. Two sets of games satisfying the coincidence property are introduced. Both are SP regions. In fact, the SP regions do not cover all games satisfying the coincidence property even for 3-person case. To enlarge the class of games with the coincidence property, the ST regions are proposed. All 3-person games with the coincidence property can be classified into 4 ST regions.

Suggested Citation

  • Chang, Chih & Tseng, Ying-Chih, 2011. "On the coincidence property," Games and Economic Behavior, Elsevier, vol. 71(2), pages 304-314, March.
    • Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:304-314
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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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    Cited by:

    1. Koji Yokote & Yukihiko Funaki, 2015. "Several bases of a game space and an application to the Shapley value," Working Papers 1419, Waseda University, Faculty of Political Science and Economics.
    2. 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.
    3. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.

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