The multilinear extension and the coalition structure value
The first author [Manage. Sci., Appl. 18, 64--79 (1972; Zbl 0239.90049)] has shown that the Shapley value of an \(n\)-person game could be obtained by integrating the partial derivatives of the multilinear extension of the game along the main diagonal of the unit cube. This technique has been used by \textit{E. Kalai} and \textit{D. Samet} [in: `The Shapley Value', Cambridge Univ. Press, Cambridge, 83--99 (1988; Zbl 0708.90098)] for the weighted Shapley value. In this paper, the authors modify the method to calculate the modified value for games with coalition structure, games which take account of the possibility that some coalitions are more likely to form than others.
scientific article; zbMATH DE number 85737