The Shapley Value for n-Person Games in Generalized Characteristic Function Form

Nowak, Adam; Radzik, Tadeusz

doi:10.1006/game.1994.1008

Cited by 58 publications

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“…Generalized characteristic functions on a player set N , introduced by Nowak and Radzik (1994), extend characteristic functions of 'classical' TU-games by assigning a real number to every ordered coalition of N . Here an ordered coalition of N is a permutation of any subset of N .…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, the two main solutions for generalized characteristic functions are the one of Nowak and Radzik (1994), which we will call the NR-value, and the one introduced by Sánchez and Bergantiños (1997), which we refer to as the SB-value. Both solutions extend the Shapley value of classical TU-games in the sense that for a generalized characteristic function that represents a classical characteristic function they yield the Shapley value of that classical game.…”

Section: Introductionmentioning

confidence: 99%

“…Both solutions extend the Shapley value of classical TU-games in the sense that for a generalized characteristic function that represents a classical characteristic function they yield the Shapley value of that classical game. Nowak and Radzik (1994) characterize their solution by efficiency, linearity and some null player property, where the last property states that players who always contribute zero when they enter an ordered coalition as last player, should get a zero payoff. Sánchez and Bergantiños (1997) criticize this null player property by arguing that in this definition a player is a null player even when it contributes to an ordered coalition in the sense that without participation of this player the coalition loses its worth.…”

Section: Introductionmentioning

confidence: 99%

“…If for any position in any ordered coalition this loss is zero, then Sánchez and Bergantiños (1997) call this a null player, and in their corresponding null player property such a player should get a zero payoff. Since this null player property is weaker than that of Nowak and Radzik (1994), Sánchez and Bergantiños (1997) added a symmetry axiom, requiring that players who are symmetric earn the same payoff, where two players are called symmetric if for every ordered coalition not containing both of them they add the same contribution when entering at the same position. They characterized their solution by efficiency, linearity, their (weak) null player property and symmetry.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Order monotonic solutions for generalized characteristic functions

Brink¹,

González–Arangüena²,

Manuel³

et al. 2014

European Journal of Operational Research

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Order monotonic solutions for generalized characteristic functions

Brink¹,

González–Arangüena²,

Manuel³

et al. 2014

European Journal of Operational Research

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“…In case of running a firm it may be appropriate to choose the internal organization of a hierarchy. In other cases, networks, communication structures or permutational structures, as studied for transferable utility games by Jackson (2005), Myerson (1977) and Nowak and Radzik (1994), respectively, or ordered structures as studied for NTU-games in van der Laan et al (1998), might fit better.…”

Section: Introductionmentioning

confidence: 99%

Socially Structured Games

2006

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ABSTRACT. We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power.We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core.We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.KEY WORDS: balancedness, core, non-transferable utility game, social stability.JEL CLASSIFICATION: C71.

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A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

Ramon

Giménez

Magaña

2007

Proc Appl Math and Mech

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We introduce a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network. The proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the directed graph that models the network. As a consequence, it is possible to offer a ranking for the nodes of directed graphs.

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The Shapley Value for n-Person Games in Generalized Characteristic Function Form

Cited by 58 publications

References 0 publications

Order monotonic solutions for generalized characteristic functions

Order monotonic solutions for generalized characteristic functions

Socially Structured Games

A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

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