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On the Aumann–Shapley value [PDF]
Positivity, 2008 This paper generalizes Theorem A in [\textit{R. J. Aumann} and \textit{L. S. Shapley}, Values of non-atomic games. Princeton, N. J.: Princeton University Press (1974; Zbl 0311.90084), p. 20], where the underlying space is an algebra of subsets isomorphic to \(([0,1], \mathcal{B})\), \(\mathcal{B}\) the Borel sets.
A. Basile +2 more
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The Shapley Value for Multigraphs
2018This paper discusses the so-called multigraph, in which multiple connections (arcs) between two given nodes and loops are possible. The authors present the concept of using Shapley values to analyse both elements (nodes and arcs) of a multigraph. The results obtained allow to evaluate the importance of a given element (node or arc) as an element of a ...
Stefan Forlicz +3 more
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ASPECTS OF EXCHANGEABILITY IN THE SHAPLEY VALUE
International Game Theory Review, 2013One of the important solution concepts in cooperative game theory is the Shapley value. The Shapley value is a probabilistic value in which each player subjectively assigns probabilities to the events which define their positions in a game. One of the most important concepts of subjective probability is the exchangeability.
R. K. Amit, Parthasarathy Ramachandran
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2003
The Shapley value, introduced in the fifties (Cf. Shapley (1953)), is one of the most interesting solution concepts in cooperative game theory which has drawn much attention. See for example A. Roth (1988). The Shapley value associates to each n-person game one (payoff) vector in ℝ n .
Bezalel Peleg, Peter Sudhölter
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The Shapley value, introduced in the fifties (Cf. Shapley (1953)), is one of the most interesting solution concepts in cooperative game theory which has drawn much attention. See for example A. Roth (1988). The Shapley value associates to each n-person game one (payoff) vector in ℝ n .
Bezalel Peleg, Peter Sudhölter
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P-Shapley: Shapley Values on Probabilistic Classifiers
Proceedings of the VLDB EndowmentThe Shapley value provides a unique approach to equitably gauge each player's contribution within a coalition and has extensive applications with various utility functions. In data valuation for machine learning, particularly for classification tasks, using classification accuracy as the utility function has become a de facto standard.
Haocheng Xia +5 more
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2019
This chapter reviews some results from the literature in which power indices related to the Shapley value are developed. First, a class of power indices for so-called effectivity functions is axiomatically characterized, based on [1]. An effectivity function describes for each coalition of players each set of alternatives such that the coalition can ...
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This chapter reviews some results from the literature in which power indices related to the Shapley value are developed. First, a class of power indices for so-called effectivity functions is axiomatically characterized, based on [1]. An effectivity function describes for each coalition of players each set of alternatives such that the coalition can ...
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2018
The value introduced by Shapley is still one of the most popular solution concepts for cooperative games. As a well-defined, always nonempty solution, it is an attractive solution that is supported by a fine axiomatisation and is a model that has also been implemented.
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The value introduced by Shapley is still one of the most popular solution concepts for cooperative games. As a well-defined, always nonempty solution, it is an attractive solution that is supported by a fine axiomatisation and is a model that has also been implemented.
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2015
In Chap. 16 set-valued solution concepts for games with transferable utilities were studied: the imputation set, core, domination core, and stable sets. In this chapter, a one-point (single-valued) solution concept is discussed: the Shapley value. It may again be helpful to first study the relevant parts of Chaps. 1 and 9.
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In Chap. 16 set-valued solution concepts for games with transferable utilities were studied: the imputation set, core, domination core, and stable sets. In this chapter, a one-point (single-valued) solution concept is discussed: the Shapley value. It may again be helpful to first study the relevant parts of Chaps. 1 and 9.
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2012
In fuzzy Multi-criteria decision-making problems, the ranking of alternatives must take into account their fuzzy scores in all criteria, the weights assigned to each decision criterion, the possible difficulties of comparing two alternatives when one is significantly better than the other on a subset of criteria, but much worse on at least one ...
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In fuzzy Multi-criteria decision-making problems, the ranking of alternatives must take into account their fuzzy scores in all criteria, the weights assigned to each decision criterion, the possible difficulties of comparing two alternatives when one is significantly better than the other on a subset of criteria, but much worse on at least one ...
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A simple algorithm for global sensitivity analysis with Shapley effects
Reliability Engineering and System Safety, 2021Takashi Goda
exaly