# Coeur et nucléolus des jeux de recouvrement

Nicolas Preux; Fatiha Bendali; Jean Mailfert; Alain Quilliot

RAIRO - Operations Research (2010)

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

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topPreux, 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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