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Multilinear extensions of games. (English) Zbl 0715.90101
The Shapley value. Essays in honor of Lloyd S. Shapley, 139-151 (1989).
[For the entire collection see Zbl 0694.00032.]
A multilinear extension of an n person cooperative game is a polynomial in n variables, defined by assigning to each coalition S the polynomial v(S)\(\prod_{i\in S}x_ i\prod_{j\not\in S}(1-x_ j)\). Multilinear extensions have applications in the theory of power indices of games, and they reflect composition of games in a useful way.
Reviewer: H.Keiding

MSC:
91A12 Cooperative games
91A06 \(n\)-person games, \(n>2\)