Semivalues: power, potential and multilinear extensions
The notions of power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of all cooperative games on a given player set. Several properties of these linear mappings are stated and their action on unanimity games is emphasized. We also relate in both case...
| Autores: | , |
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| Formato: | informe técnico |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2843 |
| Acesso em linha: | https://hdl.handle.net/2117/2843 |
| Access Level: | acceso abierto |
| Palavra-chave: | Game Theory Multilinear algebra Matrices Cooperative game Semivalue Multilinear extension Banzhaf value Shapley value Joc cooperatiu Juego cooperativo Investigació operativa -- Teoria de Jocs Jocs, Teoria de Àlgebra multilineal Matrius (Matemàtica) Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory Classificació AMS::15 Linear and multilinear algebra matrix theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Resumo: | The notions of power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of all cooperative games on a given player set. Several properties of these linear mappings are stated and their action on unanimity games is emphasized. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. |
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