Two extensions of the Shapley value for cooperative games

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Two extensions of the Shapley value for cooperative games

Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the structure of posets by means of a recursive form. In the latter setting, the Shapley value for quasi-concave games is shown to be a core-allocation.

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Cooperative Games : Core and Shapley Value

This article describes the basic elements of the cooperative approach to game theory, one of the two counterparts of the discipline. After the presentation of some basic definitions, the focus will be on the core and the Shapley value, two of the most central solution concepts in cooperative game theory. JEL classification: C7.

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Axiomatizations of the Shapley value for cooperative games on antimatroids

Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the rectricted games by antimatroids allows to unify criteria of various lines of research. ...

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Shapley value for assignment games ∗

We consider the problem of the axiomatization of the Shapley value on the class of assignment games. We show that Shapley’s original [21], Young’s [24], Chun’s [7], van den Brink’s [2], (5-6) Hart and Mas-Colell’s [12] potential function and consistency approaches and Roth’s [19] characterization do not work on the class of assignment games. We also consider Myerson’s [15] axiomatization of the...

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ژورنال

عنوان ژورنال: Mathematical Methods of Operations Research (ZOR)

سال: 2001

ISSN: 1432-2994,1432-5217

DOI: 10.1007/s001860000099