Differential marginality, van den Brink fairness, and the Shapley value

Casajus, André

doi:10.1007/s11238-009-9171-1

Cited by 64 publications

(38 citation statements)

References 7 publications

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“…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. Anonymity implies symmetry, while the converse implication is not true.…”

Section: Usual Axiomsmentioning

confidence: 99%

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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Section: Usual Axiomsmentioning

confidence: 99%

Axioms of invariance for TU-games

Béal

Rémila²,

Solal³

2014

Int J Game Theory

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“…It follows that the set of TU-games for which i obtains the payoff α ∈ R coincides with the set of TU-games v whose decomposition are of the form 3 On this point, see [8,Proposition 3]. Null player invariance is called van den Brink null player in [8] and coalitional strategic equivalence in [6]. It is shown in [6] that Null player invariance is equivalent to the axiom introduced by Chun [11] stating that for each v ∈ V N , each non-empty S ∈ 2 N and each…”

Section: Proposition 9 Fix Any Player I ∈ N a Direct-sum Decompositmentioning

confidence: 98%

Section: Proposition 9 Fix Any Player I ∈ N a Direct-sum Decompositmentioning

confidence: 99%

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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“…Later on, Nowak (1997) and Casajus (2010) employ 2-e¢ ciency to characterize the Banzhaf value, but-in contrast to Lehrer-avoid the additivity axiom by invoking marginality (Young, 1985) or di¤erential marginality (Casajus, 2009). Besides one of the amalgamation properties and the dummy player axiom, all of the above characterizations share the symmetry axiom or di¤erential marginality, where the latter is closely related to symmetry.…”

Section: Introductionmentioning

confidence: 99%