The Shapley value for cooperative games under precedence constraints

Faigle, Ulrich; Kern, Walter

doi:10.1007/bf01258278

Cited by 211 publications

(196 citation statements)

References 13 publications

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“…The properties ADD, EFF, NP and SQ degenerate to be the properties introduced by Owen [12] when we restrict the domain of CM CN in the setting of traditional games with a coalition structure. Furthermore, the property HST degenerates to be the property proposed by Faigle and Kern [23] …”

Section: Characterizations Of the Given Coalitional Valuementioning

confidence: 99%

A Coalitional Value for Multichoice Games with a Coalition Structure

Meng¹,

Zhang²

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper a new model of multichoice games with a coalition structure is proposed, which can be seen as an extension of the Owen coalition structure. A coalitional value on the given model is defined, which can be seen as an extension of the Owen value. Three axiomatic systems are studied. The first one is enlightened by Owen's characterization for the Owen value and Faigle and Kern's characterization for the Shapley value on games under precedence constraints. The second one is inspired by Bilbao's characterization for the Shapley value on games on convex geometries. The last one is an extension of Young's characterization for the Shapley value on traditional games. Furthermore, the relationship between the given coalitional value and the core of multichoice games with a coalition structure is discussed.

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Section: Characterizations Of the Given Coalitional Valuementioning

confidence: 99%

A Coalitional Value for Multichoice Games with a Coalition Structure

Meng¹,

Zhang²

2014

Appl. Math. Inf. Sci.

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“…For games on distributive lattices, Faigle and Kern (1992) showed that the Shapley value is the unique operator…”

Section: The Weber Set and The Core In Simple Gamesmentioning

confidence: 99%

“…4 Other solution concepts in simple games Faigle and Kern (1992) introduced the hierarchical strength h S (i) in distributive lattices L as follows.…”

Section: The Weber Set and The Core In Simple Gamesmentioning

confidence: 99%

“…There have been various investigations into models of cooperative games that also reflect constraints on coalition formation. See, for instance Faigle and Kern (1992) (1998), Derks and Gilles (1995) or Brink and Gilles (1996). We will restrict the feasible coalitions by using closure spaces, that is, set systems containing the set of all players and closed under intersection of coalitions.…”

Section: Introductionmentioning

confidence: 99%

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Simple games on closure spaces

Bilbao

Lebrón

Jiménez

2000

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Let N be a finite set. By a closure space we mean the family of the closed sets of a closure operator on 2 N satisfying the additional condition ∅ = ∅. A simple game on a closure space L is a function v : L → {0, 1} such that v(∅) = 0 and v (N) = 1. We assume simple games are monotonic. The coalitions are the closed sets of L and the players are the elements i ∈ N. We will give results concerning the structure of the core and the Weber set for this type of games. We show that a simple game is supermodular if and only if the game is a unanimity game and the Core (L, v) is a stable set if and only if the game v is a unanimity game.

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“…However, a more general model for cooperative games with or without transferable utilities (TU or NTU) is necessary in order to describe situations in which cooperation is restricted. In this paper we adopt the model of Faigle and Kern (1992) who assume that the set of players has a hierarchical structure generated by some partial order relation. Only those coalitions may form (are feasible) that satisfy the following condition: With any player all of her subordinates (i.e., the players preceding her according to the partial order relation) must also be members of the coalition.…”

Section: Introductionmentioning

confidence: 99%

The bounded core for games with precedence constraints

Grabisch

Sudhölter

2012

Ann Oper Res

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An element of the possibly unbounded core of a cooperative game with precedence constraints belongs to its bounded core if any transfer to a player from any of her subordinates results in payoffs outside the core. The bounded core is the union of all bounded faces of the core, it is nonempty if the core is nonempty, and it is a continuous correspondence on games with coinciding precedence constraints. If the precedence constraints generate a connected hierarchy, then the core is always nonempty. It is shown that the bounded core is axiomatized similarly to the core for classical cooperative games, namely by boundedness (BOUND), nonemptiness for zero-inessential two-person games (ZIG), anonymity, covariance under strategic equivalence (COV), and certain variants of the reduced game property (RGP), the converse reduced game property (CRGP), and the reconfirmation property. The core is the maximum solution that satisfies a suitably weakened version of BOUND together with the remaining axioms. For games with connected hierarchies, the bounded core is axiomatized by BOUND, ZIG, COV, and some variants of RGP and CRGP, whereas the core is the maximum solution that satisfies the weakened version of BOUND, COV, and the variants of RGP and CRGP.

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The Shapley value for cooperative games under precedence constraints

Cited by 211 publications

References 13 publications

A Coalitional Value for Multichoice Games with a Coalition Structure

A Coalitional Value for Multichoice Games with a Coalition Structure

Simple games on closure spaces

The bounded core for games with precedence constraints

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