Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions

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RECERCAT Home > Universitat Politècnica de Catalunya > Documents de recerca > View document

To access the full text documents, please follow this link: http://hdl.handle.net/2117/12033

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
dc.contributor.author	Carreras Escobar, Francisco
dc.contributor.author	Giménez Pradales, José Miguel
dc.date	2011-05-16
dc.identifier.citation	Carreras, F.; Giménez, J. Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions. "European journal of operational research", 16 Maig 2011, vol. 211, núm. 1, p. 148-159.
dc.identifier.citation	0377-2217
dc.identifier.citation	10.1016/j.ejor.2010.11.002
dc.identifier.uri	http://hdl.handle.net/2117/12033
dc.language.iso	eng
dc.publisher	Elsevier
dc.relation	http://www.sciencedirect.com/science/article/pii/S0377221710007514
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
dc.subject	Cooperative games (Mathematics)
dc.subject	Jocs cooperatius (Matemàtica)
dc.subject	Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
dc.title	Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. As a consequence, we derive a method to compute for any semivalue by means of multilinear extensions, in the original game and also in all its subgames, (a) the total power, (b) the potential, and (c) the allocation to each player given by the semivalue.
dc.description.abstract	Peer Reviewed

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