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

Author
Carreras, F.; Gimenez, J.
Type of activity
Journal article
Journal
European journal of operational research
Date of publication
2011-05-16
Volume
211
Number
1
First page
148
Last page
159
DOI
https://doi.org/10.1016/j.ejor.2010.11.002 Open in new window
Repository
http://hdl.handle.net/2117/12033 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0377221710007514 Open in new window
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 s...
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.
Group of research
GRTJ - Game Theory Research Group