Weighted allocation rules for standard fixed tree games

In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler e...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Germany), 2004-06, Vol.59 (2), p.249-270
Main Authors: Bj rndal, Endre, Koster, Maurice, Tijs, Stef
Format: Article
Language:English
Subjects:
Airports
Econometrics
Game theory
Games
Mathematical analysis
Mathematical models
Operations research
Studies
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Summary:In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995). We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation species a weighted Shapley value (Kalai and Samet (1988) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights. [PUBLICATION ABSTRACT]
ISSN:1432-2994
1432-5217
DOI:10.1007/s001860300324