An axiomatization of the Shapley value using a fairness property

Brink, René van den

doi:10.1007/s001820100079

Cited by 113 publications

(52 citation statements)

References 14 publications

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“…Our new axioms do not imply nor are implied by the axioms of fairness introduced by van den Brink [21] or marginality proposed by Young [24]. The appendix proves these statements.…”

Section: Corollarymentioning

confidence: 63%

“…Casajus [3] proves that marginality and the axiom coalitional strategic equivalence introduced by Chun [4] are equivalent (see Proposition 3 and footnote 3 on page 169) and van den Brink [21] shows that fairness does not imply nor is implied by marginality. We also refer to Casajus [3] for a comparison with the closely related axiom of differential marginality, which is proved to be equivalent to fairness.…”

Section: Usual Axiomsmentioning

confidence: 97%

“…The nullifying player property, fairness, marginality and are studied in van den Brink [22], van den Brink [21], Young [24] respectively. Casajus [3] proves that marginality and the axiom coalitional strategic equivalence introduced by Chun [4] are equivalent (see Proposition 3 and footnote 3 on page 169) and van den Brink [21] shows that fairness does not imply nor is implied by marginality.…”

Section: Usual Axiomsmentioning

confidence: 99%

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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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“…Our new axioms do not imply nor are implied by the axioms of fairness introduced by van den Brink [21] or marginality proposed by Young [24]. The appendix proves these statements.…”

Section: Corollarymentioning

confidence: 63%

Section: Usual Axiomsmentioning

confidence: 97%

Section: Usual Axiomsmentioning

confidence: 99%

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Axioms of invariance for TU-games

Béal

Rémila²,

Solal³

2014

Int J Game Theory

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“…This is a weakening of fairness 2 as used by van den Brink (2001) in axiomatizing the Shapley value.…”

Section: Characterizations For Two-player Gamesmentioning

confidence: 99%

“…Therefore, we consider a weak covariance which requires that the payoffs of all players change by the same amount if to each coalition we add a constant times the number of players in the coalition. This property can also be seen as a weakening of the fairness axiom in van den Brink (2001). In this paper, we also use another weakening of fairness requiring that the payoffs of all players change by the same amount when we only change the worth of the 'grand coalition'.…”

mentioning

confidence: 99%

Consistency, population solidarity, and egalitarian solutions for TU-games

Brink¹,

Chun

Funaki

et al. 2016

Theory Decis

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A (point-valued) solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution (which allocates the worth of the 'grand coalition' consisting of all players equally over all players) and the center-of-gravity of the imputation-set value (which first assigns every player its singleton worth and then allocates the remainder of the worth of the grand coalition, N , equally over all players). The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value (which first assigns every player its contribution to the 'grand coalition' and then allocates the remainder equally over all players). We provide characterizations of the two classes of solutions using either population solidarity or a reduced game consistency in addition to other standard properties.

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Can cooperative game theory solve the low‐risk puzzle?

Auer

Hiller

2018

Int. J Fin Econ

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In this article, we illustrate that cooperative game theory may have the potential to solve the low‐risk puzzle, which has become one of the most important in modern finance because its implication of a negative risk‐return trade‐off poses a challenge to traditional models of asset prices. Using several simulation settings, we highlight that quantifying risk by means of assets' Shapley values, that is, assets' contributions to overall portfolio risk, instead of classic measures supplies a (more) positive risk‐return relationship in many practically relevant cases. This is partially attributable to the fact that the game‐theoretic risk measure captures more investment‐relevant information than commonly used alternatives.

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An axiomatization of the Shapley value using a fairness property

Cited by 113 publications

References 14 publications

Axioms of invariance for TU-games

Axioms of invariance for TU-games

Consistency, population solidarity, and egalitarian solutions for TU-games

Can cooperative game theory solve the low‐risk puzzle?

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