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Exploration de la valeur de Shapley et des indices d'interaction pour les jeux définis sur des ensembles ordonnés

Abstract : Lattice functions appear to be an essential tool in operations research, opening new areas in the fields of cooperative game theory (players or agents form coalitions in games), and decision making (capacities or fuzzy measures are defined over some coalitions structures of criteria). The thesis aims at investigating solution concepts for games defined on general coalitions structures. In this purpose, we propose several generalizations of the Shapley value with axiomatizations for multichoice games, games over distributive lattices, and regular games. The interaction index quantifies the genuine contribution of a coalition with reference to all its subcoalitions. Mathematically, it is an extension of the Shapley value, and it involves the derivatives of the game. We propose some axiomatizations of the Shapley interaction index for bi-cooperative games, and some means for computing it from games in transferable utility form, and vice versa.
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Submitted on : Thursday, April 17, 2008 - 5:37:35 PM
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Fabien Lange. Exploration de la valeur de Shapley et des indices d'interaction pour les jeux définis sur des ensembles ordonnés. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2007. Français. ⟨tel-00274302⟩

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