A Class of Social-Shapley Values of Cooperative Games with Graph Structure

  • Hui YangEmail author
  • Hao Sun
  • Genjiu Xu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1082)


This paper is devoted to a class of Social-Shapley values for cooperative games with graph structure. The Social-Shapley value compromises the utilitarianism of the Shapley value and the egalitarianism of the Solidarity value, in which the sociality is reflected by the Solidarity value. Through defining the corresponding properties in graph-restricted games, the paper axiomatically characterizes the Social-Shapley value when the coefficient is given exogenously. Moreover, we axiomatize the class of all possible Social-Shapley values in the graph-restricted games.


Cooperative games Graph structure The Social-Shapley value Axiomatization 



This research has been supported by the National Natural Science Foundation of China (Grant No. 71571143), the Science and Technology Research and Development Program in Shaanxi Province of China (Grant Nos. 2017GY-095, 2017JM5147).


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Department of ScienceXi’an University of Science and TechnologyXi’anChina

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