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Coeur et nucléolus des jeux de recouvrement

Published online by Cambridge University Press:  15 August 2002

Nicolas Preux ,
Fatiha Bendali ,
Jean Mailfert  and
Alain Quilliot
Nicolas Preux
Affiliation:
France Telecom – CNET, 38-40 avenue du Général Leclerc, 92794 Issy-les-Moulineaux Cedex 9, France.
Fatiha Bendali
Affiliation:
LIMOS, Université Blaise Pascal, 63174 Aubière Cedex, France.
Jean Mailfert
Affiliation:
LIMOS, Université Blaise Pascal, 63174 Aubière Cedex, France.
Alain Quilliot
Affiliation:
LIMOS, Université Blaise Pascal, 63174 Aubière Cedex, France.
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Abstract

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between theplayers can be done using the core concept, that is the set of all undominated cost allocations which prevent playersfrom grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integercovering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize itsallocations using linear programming duality. We also discuss a special allocation, called the nucleolus. Wecharacterize that allocation and show that it can be computed in polynomial time using a column generation method.

Keywords

Théorie des jeuxprogrammation linéaire réelle et entièregénération de colonnescomplexité.Game theorycontinuous and integer linear programmingcolumn generationcomplexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 34 , Issue 3 , July 2000 , pp. 363 - 383
Copyright
© EDP Sciences, 2000

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