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- Title
Matrix Expression of Shapley Value in Graphical Cooperative Games.
- Authors
Wang, Yuanhua; Alsaadi, Fuad E.; Liu, Zheng; Wu, Xiaomeng; Liu, Xiyu
- 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.
- Subjects
NONCOOPERATIVE games (Mathematics); GAMES; MATRIX multiplications; TELECOMMUNICATION systems; MATRICES (Mathematics); COALITIONS
- Publication
Mathematical Problems in Engineering, 2020, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2020/2045654