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