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Shapley mappings and the cumulative value for \(n\)-person games with fuzzy coalitions. (English) Zbl 1138.91320

Summary: We prove existence and uniqueness of the so-called Shapley mapping, which is a solution concept for a class of \(n\)-person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a “cumulative value” that is the “sum” of all coalitional allocations for whose computation we provide an explicit formula.

MSC:

91A12 Cooperative games
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