The axiomatic approach to three values in games with coalition structure

Gómez-Rúa, María; Vidal-Puga, Juan

doi:10.1016/j.ejor.2010.05.014

Cited by 36 publications

(11 citation statements)

References 46 publications

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“…Thus, it is deduced that the value φ does not satisfy the property of null player 4 . Notice, however, that we consider situations in which the players represent groups.…”

Section: Example 1 Consider the Gamementioning

confidence: 99%

Balanced per capita contributions and level structure of cooperation

Gómez-Rúa

Vidal-Puga

2009

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“…Thus, it is deduced that the value φ does not satisfy the property of null player 4 . Notice, however, that we consider situations in which the players represent groups.…”

Section: Example 1 Consider the Gamementioning

confidence: 99%

Balanced per capita contributions and level structure of cooperation

Gómez-Rúa

Vidal-Puga

2009

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“…So a null player is only a null in the coalition function and not necessary in the weight system for coalitions. For further information on this area see also Gómez-Rúa and Vidal-Puga (2010) and Gómez-Rúa and Vidal-Puga (2011).…”

Section: Resultsmentioning

confidence: 99%

Weighted Shapley hierarchy levels values

Besner

2019

Operations Research Letters

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In this paper we present a new class of values for cooperative games with level structure. We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted Shapley values. Our first axiomatization is an generalisation of the axiomatization given in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by efficiency and weighted balanced contributions. The second axiomatization is completely new and extends the axiomatization of the weighted Shapley values introduced in Hart and Mas-Colell (1989) by weighted standardness for two player games and consistency. As a corollary we obtain a new axiomatization of the Shapley levels value.

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“…There is an extensive literature on axiomatic characterization of coalitional values: Aumann and Drèze (1974), Owen (1977), Hart and Kurz (1983), Levy and McLean (1989), Alonso-Meijide and FiestrasJaneiro (2002), Amer et al (2002), Młodak (2003), Carreras and Puente (2006), Kamijo (2009, in press), Gómez-Rúa and Vidal-Puga (2010) and Calvo and Gutiérrez (2010), among others.…”

Section: Introductionmentioning

confidence: 99%

The Harsanyi paradox and the “right to talk” in bargaining among coalitions

Vidal-Puga

2012

Mathematical Social Sciences

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a b s t r a c tWe describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own ''right to talk'' when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.

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The axiomatic approach to three values in games with coalition structure

Cited by 36 publications

References 46 publications

Balanced per capita contributions and level structure of cooperation

Balanced per capita contributions and level structure of cooperation

Weighted Shapley hierarchy levels values

The Harsanyi paradox and the “right to talk” in bargaining among coalitions

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