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Fast computation of the leastcore and prenucleolus of cooperative games

Published online by Cambridge University Press:  20 August 2008

Joseph Frédéric Bonnans  and
Matthieu André
Joseph Frédéric Bonnans
Affiliation:
Inria-Futurs and Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France; Frederic.Bonnans@inria.fr
Matthieu André
Affiliation:
Direction Optimisation Amont-Aval Trading, EDF, 1 Place Pleyel, 93282 Saint-Denis Cedex, France; matthieu.andre@edfgdf.fr
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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.

Keywords

Cooperative gamescoalitionsconstraint generationdecompositionconvex production gamessymmetric gamesaggregate playersnucleolus.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 3 , July 2008 , pp. 299 - 314
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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