Matrix expression of Myerson Value

This paper explores the matrix expression of the Myerson value, a variant of the Shapley value within a class of cooperative games subject to graph constraints. A systematic and comprehensive matrix framework is proposed, encompassing the characteristic function of cooperative games, the worths of coalitions in graph-restricted games, and the axioms governing the Myerson value. Utilizing this framework, the paper offers a rigorous reproof validating the satisfaction of the two axioms by the Myerson value and establishes its uniqueness within the context of matrix representation. Additionally, a novel formula is presented for computing the Shapley value through matrix construction, simplifying the computational process compared to the previous matrix formulations. Finally, the provided formula is applied to calculate the Myerson value of a supply chain.