The heart and nucleolus of cooperative games

The heart and nucleolus of cooperative games

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Article ID: iaor20052741
Country: France
Volume: 34
Issue: 3
Start Page Number: 363
End Page Number: 383
Publication Date: Jul 2000
Journal: RAIRO Operations Research
Authors: , , ,
Keywords: programming: integer
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.

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