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Generating functions for computing the Myerson value. (English) Zbl 1007.91005

Summary: The complexity of a computational problem is the order of computational resources which are necessary and sufficient to solve the problem. The algorithm complexity is the cost of a particular algorithm. We say that a problem has polynomial complexity if its computational complexity is a polynomial in the measure of input size. We introduce polynomial time algorithms based in generating functions for computing the Myerson value in weighted voting games restricted by a tree. Moreover, we apply the new generating algorithm for computing the Myerson value in the Council of Ministers of the European Union restricted by a communication structure.

MSC:

91A12 Cooperative games
65Y20 Complexity and performance of numerical algorithms

Software:

Mathematica
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