The value of a player in n-person games

Abstract

. The article decomposes the Shapley value into a value matrix which gives the value of every player to every other player in n-person games. Element Φ_ij(v) in the value matrix is positive, zero, or negative, dependent on whether row player i is beneficial, has no impact, or is not beneficial for column player j. The elements in each row and in each column of the value matrix sum up to the Shapley value of the respective player. The value matrix is illustrated by the voting procedure in the European Council of Ministers 1981–1995.