The shapley value on some lattices of monotonic games

Ezra Einy

doi:10.1016/0165-4896(88)90025-X

The shapley value on some lattices of monotonic games

Ezra Einy

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

It is shown that the restriction of the Shapley value to the lattice of all monotonic games whose range is contained in an arbitrary set of non-negative real numbers (which contains 0) can be uniquely characterized by the axioms that were given by Dubey (in order to characterize the Shapley value on the class of monotonic simple games). We also derive formulas for the Shapley-Shubik and Banzhaf power indices in terms of the minimal winning coalitions of the game.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Mathematical Social Sciences
Volume	15
Issue number	1
DOIs	https://doi.org/10.1016/0165-4896(88)90025-X
State	Published - 1 Jan 1988
Externally published	Yes

Keywords

Banzhaf value
Monotonic game
Shapley value
simple game
valuation

ASJC Scopus subject areas

Sociology and Political Science
Social Sciences (all)
Psychology (all)
Statistics, Probability and Uncertainty

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10.1016/0165-4896(88)90025-X

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AB - It is shown that the restriction of the Shapley value to the lattice of all monotonic games whose range is contained in an arbitrary set of non-negative real numbers (which contains 0) can be uniquely characterized by the axioms that were given by Dubey (in order to characterize the Shapley value on the class of monotonic simple games). We also derive formulas for the Shapley-Shubik and Banzhaf power indices in terms of the minimal winning coalitions of the game.

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KW - Monotonic game

KW - Shapley value

KW - simple game

KW - valuation

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ER -

The shapley value on some lattices of monotonic games

Abstract

Keywords

ASJC Scopus subject areas

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