Shapley mappings and the cumulative value for n-person games with fuzzy coalitions |
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Authors: | Dan Butnariu,Tomá &scaron Kroupa |
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Affiliation: | 1. Department of Mathematics, University of Haifa, 31 905 Haifa, Israel;2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodárenskou vě?í 4, 182 08 Prague, Czech Republic |
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Abstract: | In this paper 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. |
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Keywords: | Coalition Cumulative value Fuzzy coalition n-Person cooperative game Shapley value |
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