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Matrix Expression of Shapley Value in Graphical Cooperative Games

Author

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  • Yuanhua Wang
  • Fuad E. Alsaadi
  • Zheng Liu
  • Xiaomeng Wu
  • Xiyu Liu

Abstract

This paper studies a class of cooperative games, called graphical cooperative games, where the internal topology of the coalition depends on a prescribed communication graph among players. First, using the semitensor product of matrices, the value function of graphical cooperative games can be expressed as a pseudo-Boolean function. Then, a simple matrix formula is provided to calculate the Shapley value of graphical cooperative games. Finally, some practical examples are presented to illustrate the application of graphical cooperative games in communication-based coalitions and establish the significance of the Shapley value in different communication networks.

Suggested Citation

  • Yuanhua Wang & Fuad E. Alsaadi & Zheng Liu & Xiaomeng Wu & Xiyu Liu, 2020. "Matrix Expression of Shapley Value in Graphical Cooperative Games," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, May.
    • Handle: RePEc:hin:jnlmpe:2045654
    DOI: 10.1155/2020/2045654
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