Weak addition invariance and axiomatization of the weighted Shapley value

Yokote, Koji

doi:10.1007/s00182-014-0429-7

Cited by 12 publications

(10 citation statements)

References 10 publications

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“…Furthermore, these characterizations are obtained without the classical axioms of Efficiency, Linearity/Additivity, Anonymity/Symmetry. Yokote [24] introduces a new axiom of addition invariance. This axiom, called Strong addition invariance, states that if the worths of all coalitions whose intersection with a fixed coalition is a singleton, change by the same amount, then the payoff vector should not change.…”

Section: Corollary 1 the Allocation Rules Ed Esd And Sh Satisfy Thementioning

confidence: 99%

“…We provide an alternative and direct proof of the fact that these TU-games are linearly independent. Then, Yokote [24] shows that the combination of Strong addition invariance and the Dummy player axiom characterizes the Shapley value [22]. We show that the Dummy player axiom is stronger than necessary in the sense that the kernel of the Shapley value and the subspace of TU-games for which a player is dummy are not in direct sum.…”

Section: Introductionmentioning

confidence: 96%

“…Section 4 exploits this method to provide new characterizations of several allocation rules. Section 5 revisits the approach developed by Yokote [24]. Section 6 deals with the logical independence of the axioms used in the characterizations.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 provides preliminaries. It introduces the axioms of (Strong) Addition invariance and Transfer invariance and summarizes the main results obtained in [2] and [24]. Section 3 is devoted to the decomposition method.…”

Section: Introductionmentioning

confidence: 99%

“…In a fourth step, we revisit the approach by Yokote [24] who introduces a new axiom of invariance, called Strong addition Invariance, inspired by the axiom of Addition invariance. It requires that the payoffs distributed to the players in a TU-game do not change if some specific TU-games are added.…”

Section: Introductionmentioning

confidence: 99%

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A decomposition of the space of TU-games using addition and transfer invariance

Béal

Rémila²,

Solal³

2015

Discrete Applied Mathematics

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a b s t r a c tIn Béal et al. (forthcoming) two new axioms of invariance, called Addition invariance and Transfer invariance respectively, are introduced to design allocation rules for TU-games. Here, we derive direct-sum decompositions of the linear space of TU-games by using the TU-games selected to construct the operations of Addition and Transfer. These decompositions allow us to recover previous characterization results obtained by Béal et al. (forthcoming), to provide new characterizations of well-known (class of) allocation rules and also to design new allocation rules.

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Section: Corollary 1 the Allocation Rules Ed Esd And Sh Satisfy Thementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A decomposition of the space of TU-games using addition and transfer invariance

Béal

Rémila²,

Solal³

2015

Discrete Applied Mathematics

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Bases and Transforms of Set Functions

Grabisch

2016

Studies in Fuzziness and Soft Computing

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International audienceThe paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic dual-ity between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral

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Axioms of invariance for TU-games

Béal

Rémila²,

Solal³

2014

Int J Game Theory

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We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TU-games. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used.

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Weak addition invariance and axiomatization of the weighted Shapley value

Cited by 12 publications

References 10 publications

A decomposition of the space of TU-games using addition and transfer invariance

A decomposition of the space of TU-games using addition and transfer invariance

Bases and Transforms of Set Functions

Axioms of invariance for TU-games

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