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

## Abstract

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.

## Keywords

Cooperative games Graph structure The Social-Shapley value Axiomatization## Notes

### Acknowledgement

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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