# Coeur et nucléolus des jeux de recouvrement

• Volume: 34, Issue: 3, page 363-383
• ISSN: 0399-0559

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## Abstract

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

## How to cite

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Preux, Nicolas, et al. "Coeur et nucléolus des jeux de recouvrement." RAIRO - Operations Research 34.3 (2010): 363-383. <http://eudml.org/doc/197798>.

@article{Preux2010,
abstract = { A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming duality. We also discuss a special allocation, called the nucleolus. We characterize that allocation and show that it can be computed in polynomial time using a column generation method. },
author = {Preux, Nicolas, Bendali, Fatiha, Mailfert, Jean, Quilliot, Alain},
journal = {RAIRO - Operations Research},
keywords = {Théorie des jeux; programmation linéaire réelle et entière; génération de colonnes; complexité.; Game theory; continuous and integer linear programming; column generation; complexity.; core; linear integer covering problem; nucleolus; polynomial time; column generation},
language = {eng},
month = {3},
number = {3},
pages = {363-383},
publisher = {EDP Sciences},
title = {Coeur et nucléolus des jeux de recouvrement},
url = {http://eudml.org/doc/197798},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Preux, Nicolas
AU - Bendali, Fatiha
AU - Mailfert, Jean
AU - Quilliot, Alain
TI - Coeur et nucléolus des jeux de recouvrement
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 3
SP - 363
EP - 383
AB - A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming duality. We also discuss a special allocation, called the nucleolus. We characterize that allocation and show that it can be computed in polynomial time using a column generation method.
LA - eng
KW - Théorie des jeux; programmation linéaire réelle et entière; génération de colonnes; complexité.; Game theory; continuous and integer linear programming; column generation; complexity.; core; linear integer covering problem; nucleolus; polynomial time; column generation
UR - http://eudml.org/doc/197798
ER -

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