The bargaining set of four-person balanced games

It is well known that in three-person transferable-utility cooperative games the bargaining set [physics M-matrix]i1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which...

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Bibliographic Details
Published in:International journal of game theory 2002-09, Vol.31 (1), p.1-11
Main Author: Solymosi, Tamás
Format: Article
Language:English
Subjects:
Bargaining
Coalitions
Cooperation
Economic theory
Game theory
Games
Linear programming
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Summary:It is well known that in three-person transferable-utility cooperative games the bargaining set [physics M-matrix]i1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set [physics M-matrix]i1 (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set [physics M-matrix]i1. Our discussion employs a generalization of balancedness to games with coalition structures.
ISSN:0020-7276
1432-1270
DOI:10.1007/s001820200102