A characterization of the position value*

Slikker, Marco

doi:10.1007/s00182-005-0211-y

Cited by 70 publications

(53 citation statements)

References 7 publications

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“…Also the position value, denoted by γ(v, L), introduced for the class of all graph games and characterized on the class of cycle-free graph games in Borm et al [2], does not need to be stable. Slikker [16] characterizes the position value on the class of graph games as the unique solution satisfying component efficiency and balanced total threats, saying that the total threat of any player i towards another player j is equal to the total threat of player j towards player i. The total threat of a player i towards another player j is defined as the sum over all links of player i of the payoff differences player j experiences if such a link is broken, i.e.…”

Section: Corollary 41mentioning

confidence: 99%

“…In the latter paper also another solution for graph games has been proposed, the so-called positional value, see also Meessen [11]. This value is also characterized by component efficiency and by balanced total threats, see Slikker [16]. The balanced total threat property says that the total threat of any player towards another player equals to the total threat of that player towards the first player, where the total threat of a player towards another player is the sum over all links of the first player of payoff differences the second player experiences if such a link is broken.…”

Section: Introductionmentioning

confidence: 99%

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The Component Fairness Solution for Cycle-free Graph Games

2006

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In this paper we study cooperative games with limited cooperation possibilities, represented by an undirected cycle-free communication graph. Players in the game can cooperate if and only if they are connected in the graph, i.e. they can communicate with one another. We introduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretation of component fairness is that deleting a link between two players yields for both resulting components the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. The component fairness solution is always in the core of the restricted game in case the game is superadditive and can be easily computed as the average of n specific marginal vectors, where n is the number of players. We also show that the component fairness solution can be generated by a specific distribution of the Harsanyi-dividends.

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Section: Corollary 41mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Component Fairness Solution for Cycle-free Graph Games

2006

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“…For the allocation rules, we will focus in this paper on the Position value, introduced by Meessen (1988) and further analyzed by Borm et al (1992) and Slikker (2005) for the ex post stage and generalized by Ghintran et al (2010) for the ex ante stage, and the graph-χ-value, introduced by Casajus (2009) for the ex post stage. We will define the graph-χ-value for the ex ante stage.…”

Section: Introductionmentioning

confidence: 99%

A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements

Belau

2012

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors' own opinions and do not necessarily refl ect those of the editors. (Meessen (1988) and Borm et al. (1992)) and graph--value (Casajus (2009) Terms of use: Documents in Ruhr Economic Papers #326

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“…The position value is another solution for the games proposed by Borm et al [3]. This value is characterized by component efficiency and balanced link contribution, which is in the same spirit as balanced contribution, see Slikker [9]. Both the Myerson value and the position value are based on the Shapley value.…”

Section: Introductionmentioning

confidence: 99%

Parameterized fairness axioms on cycle-free graph games

2011

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Abstract. In this paper we study cooperative transferable utility games with communication structure represented by an undirected graph, i.e., a group of players can cooperate only if they are connected on the graph. This type of games is called graph games and the best-known solution for them is the Myerson value, characterized by component efficiency and fairness. Recently on cycle-free graph games, the average tree solution has been proposed and it is characterized by component efficiency and component fairness. We propose -parameterized fairness that incorporates the preceding fairness axioms on cycle-free graph games and show the existence and the uniqueness of a solution satisfying component efficiency and our fairness for any nonnegative parameter . We then discuss a relationship between the existing and our proposed solutions by a numerical example.

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A characterization of the position value*

Abstract: Communication situation, position value, characterization, C71,

Cited by 70 publications

References 7 publications

The Component Fairness Solution for Cycle-free Graph Games

The Component Fairness Solution for Cycle-free Graph Games

A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements

Parameterized fairness axioms on cycle-free graph games

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