The Axiomatic Characterization of the Grey Shapley Value
One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characteri...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/51 |
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| Summary: | One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characterize and redefine this value in cooperative games where coalition values are grey numbers. In this study, the grey Shapley value is characterized by the following axioms: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-gain loss, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-null player, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-differential marginality. Finally, this study concludes with an investigation of some applications involving production costs. This study is based on an investigation of the costs incurred when milk producers collaborate. |
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| ISSN: | 2075-1680 |