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Preorders in simple games

Author
Freixas, J.; Pons, M.
Type of activity
Book chapter
Book
Transactions on computational collective intelligence XXVII
First page
63
Last page
73
Publisher
Springer
Date of publication
2017-11-25
ISBN
978-3-319-70646-7 Open in new window
DOI
https://doi.org/10.1007/978-3-319-70647-4_5 Open in new window
Repository
http://hdl.handle.net/2117/113429 Open in new window
URL
https://link.springer.com/chapter/10.1007/978-3-319-70647-4_5 Open in new window
Abstract
Any power index defines a total preorder in a simple game and, thus, induces a hierarchy among its players. The desirability relation, which is also a preorder, induces the same hierarchy as the Banzhaf and the Shapley indices on linear games, i.e., games in which the desirability relation is total. The desirability relation is a sub–preorder of another preorder, the weak desirability relation, and the class of weakly linear games, i.e., games for which the weak desirability relation is total,...
Citation
Freixas, J., Pons, M. Preorders in simple games. A: "Transactions on computational collective intelligence XXVII". Berlín: Springer, 2017, p. 63-73.
Keywords
Desirability, Linear game, Power index, Preorder, Simple game, Weak desirability, Weakly linear game
Group of research
GRTJ - Game Theory Research Group

Participants