Fast computation of the leastcore and prenucleolus of cooperative games

Joseph Frédéric Bonnans; Matthieu André

RAIRO - Operations Research (2008)

  • Volume: 42, Issue: 3, page 299-314
  • ISSN: 0399-0559

Abstract

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The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous coalitions. We also study the computation of prenucleolus, and display encouraging numerical results.

How to cite

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Bonnans, Joseph Frédéric, and André, Matthieu. "Fast computation of the leastcore and prenucleolus of cooperative games." RAIRO - Operations Research 42.3 (2008): 299-314. <http://eudml.org/doc/250422>.

@article{Bonnans2008,
abstract = { The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous coalitions. We also study the computation of prenucleolus, and display encouraging numerical results. },
author = {Bonnans, Joseph Frédéric, André, Matthieu},
journal = {RAIRO - Operations Research},
keywords = {Cooperative games; coalitions; constraint generation; decomposition; convex production games; symmetric games; aggregate players; nucleolus.; cooperative games; convex production games; nucleolus},
language = {eng},
month = {8},
number = {3},
pages = {299-314},
publisher = {EDP Sciences},
title = {Fast computation of the leastcore and prenucleolus of cooperative games},
url = {http://eudml.org/doc/250422},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Bonnans, Joseph Frédéric
AU - André, Matthieu
TI - Fast computation of the leastcore and prenucleolus of cooperative games
JO - RAIRO - Operations Research
DA - 2008/8//
PB - EDP Sciences
VL - 42
IS - 3
SP - 299
EP - 314
AB - The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous coalitions. We also study the computation of prenucleolus, and display encouraging numerical results.
LA - eng
KW - Cooperative games; coalitions; constraint generation; decomposition; convex production games; symmetric games; aggregate players; nucleolus.; cooperative games; convex production games; nucleolus
UR - http://eudml.org/doc/250422
ER -

References

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  9. Jörg Oswald, Jean Derks and Hans Peters, Prenucleolus and nucleolus of a cooperative game: characterizations by tight coalitions. In 3rd International Conference on Approximation and Optimization in the Caribbean (Puebla, 1995), Aportaciones Mat. Comun. vol. 24, Soc. Mat. Mexicana, México (1998) 197–216.  Zbl1005.91017
  10. G. Owen, On the core of linear production games. Math. Program.9 (1975) 358–370.  Zbl0318.90060
  11. N. Preux, F. Bendali, J. Mailfert, and A. Quilliot. Cœur et nucléolus des jeux de recouvrement. RAIRO-Oper. Res.34 (2000) 363–383.  Zbl1006.91007
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