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Nodes of directed graphs ranked by solutions defined on cooperative games
Amer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, Antonio
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
Hierarchical structures, transportation systems, communication networks and even sports competitions can be modeled by means of directed graphs. Since digraphs without a predefined game are considered, the main part of the work is devoted to establish conditions on cooperative games so that they can be used to measure accessibility to the nodes. Games that satisfy desirable properties are called test games. Each ranking on the nodes is then obtained according to a pair formed by a test game and a solution defined on cooperative games whose utilities are given for every ordered coalition. Solutions here proposed are extensions of the wide family of semivalues to games in generalized characteristic function form.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
Game theory
Jocs, Teoria de
Classificació AMS::15 Linear and multilinear algebra; matrix theory
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
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