The multilinear extension and the coalition structure value
type: Item
instance of: scholarly article
title: The multilinear extension and the coalition structure value
zbMATH Open document ID: 0816.90142
DOI: 10.1016/0899-8256(92)90038-T
author: Eyal Winter
author: Guillermo Owen
published in: Games and Economic Behavior
publication date: 1993-01-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 85737
zbMATH Keywords: Shapley value
zbMATH Keywords: modified value
MaRDI profile type: Publication
cites work: Endogenous Formation of Coalitions
cites work: On weighted Shapley values
cites work: Multilinear Extensions of Games
cites work: Q4178815
cites work: Q5817870
cites work: A value for cooperative games with levels structure of cooperation
full work available at URL: 0899-8256(92)90038-t
OpenAlex ID: W1976859298
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description: scientific article; zbMATH DE number 85737