Marginalist and efficient values for TU games

We derive an explicit formula for a marginalist and efficient value for TU game which possesses the null-player property and is either continuous or monotonic. We show that every such value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic...

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Published inMathematical social sciences Vol. 38; no. 1; pp. 45 - 54
Main Author Khmelnitskaya, Anna B.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.1999
Elsevier
SeriesMathematical Social Sciences
Subjects
Axiomatic characterization
Economic efficiency
Efficiency
Marginalism
Mathematical economics
Transferable utility game
Utility functions
Value
Values
Value
Efficiency
Transferable utility game
Marginalism
Axiomatic characterization
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Abstract We derive an explicit formula for a marginalist and efficient value for TU game which possesses the null-player property and is either continuous or monotonic. We show that every such value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the null-player property coincides with the set of random-order values, and, thereby, the last statement provides an axiomatization without the linearity axiom for the latter which is similar to that of Young for the Shapley value. Another axiomatization without linearity for random-order values is provided by marginalism, efficiency, monotonicity and covariance.
AbstractList We derive an explicit formula for a marginalist and efficient value for TU game which possesses the null-player property and is either continuous or monotonic. We show that every such value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the null-player property coincides with the set of random-order values, and, thereby, the last statement provides an axiomatization without the linearity axiom for the latter which is similar to that of Young for the Shapley value. Another axiomatization without linearity for random-order values is provided by marginalism, efficiency, monotonicity and covariance.
Author Khmelnitskaya, Anna B.
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Cites_doi 10.1007/BF01240250
10.1017/CBO9780511528446.008
10.1016/0899-8256(89)90014-6
10.1007/BF01769885
10.1016/0022-0531(86)90088-8
10.1515/9781400881970-018
10.1007/BF01240278
10.1007/BF01262517
10.1016/B978-0-12-370182-4.50012-X
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Keywords Value
Efficiency
Transferable utility game
Marginalism
Axiomatic characterization
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StartPage 45
SubjectTerms Axiomatic characterization
Economic efficiency
Efficiency
Marginalism
Mathematical economics
Transferable utility game
Utility functions
Value
Values
Title Marginalist and efficient values for TU games
URI https://dx.doi.org/10.1016/S0165-4896(98)00045-6
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