Decomposable Effectivity Functions

G.J.M. Otten

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Abstract

Decomposable effectivity functions are introduced as an extension of additive effectivity functions. Whereas additive effectivity functions are determined by pairs of additive TU-games, decomposable effectivity functions are generated by pairs of TU-games that need not be additive. It turns out that the class of decomposable effectivity functions does not only contain the class of additive effectivity functions but it also contains the class of effectivity functions corresponding to simple games and the class of effectivity functions corresponding to veto functions. We examine relations between properties of decomposable effectivity functions and the TU-games by which they are generated. It turns out that a decomposable effectivity function is stable whenever it can be generated by a pair of balanced TU-utility games. Finally, we provide two characterizations of decomposable effectivity functions.
Original languageEnglish
PublisherCentER
Volume1995-26
Publication statusPublished - 1995

Publication series

NameCentER Discussion Paper
Volume1995-26

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Decomposable
TU Game
Additive Function
Simple Game
Game
Class

Cite this

Otten, G. J. M. (1995). Decomposable Effectivity Functions. (CentER Discussion Paper; Vol. 1995-26). CentER.
Otten, G.J.M. / Decomposable Effectivity Functions. CentER, 1995. (CentER Discussion Paper).
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Otten, GJM 1995 'Decomposable Effectivity Functions' CentER Discussion Paper, vol. 1995-26, CentER.

Decomposable Effectivity Functions. / Otten, G.J.M.

CentER, 1995. (CentER Discussion Paper; Vol. 1995-26).

Research output: Working paperDiscussion paperOther research output

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T1 - Decomposable Effectivity Functions

AU - Otten, G.J.M.

PY - 1995

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N2 - Decomposable effectivity functions are introduced as an extension of additive effectivity functions. Whereas additive effectivity functions are determined by pairs of additive TU-games, decomposable effectivity functions are generated by pairs of TU-games that need not be additive. It turns out that the class of decomposable effectivity functions does not only contain the class of additive effectivity functions but it also contains the class of effectivity functions corresponding to simple games and the class of effectivity functions corresponding to veto functions. We examine relations between properties of decomposable effectivity functions and the TU-games by which they are generated. It turns out that a decomposable effectivity function is stable whenever it can be generated by a pair of balanced TU-utility games. Finally, we provide two characterizations of decomposable effectivity functions.

AB - Decomposable effectivity functions are introduced as an extension of additive effectivity functions. Whereas additive effectivity functions are determined by pairs of additive TU-games, decomposable effectivity functions are generated by pairs of TU-games that need not be additive. It turns out that the class of decomposable effectivity functions does not only contain the class of additive effectivity functions but it also contains the class of effectivity functions corresponding to simple games and the class of effectivity functions corresponding to veto functions. We examine relations between properties of decomposable effectivity functions and the TU-games by which they are generated. It turns out that a decomposable effectivity function is stable whenever it can be generated by a pair of balanced TU-utility games. Finally, we provide two characterizations of decomposable effectivity functions.

M3 - Discussion paper

VL - 1995-26

T3 - CentER Discussion Paper

BT - Decomposable Effectivity Functions

PB - CentER

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Otten GJM. Decomposable Effectivity Functions. CentER. 1995. (CentER Discussion Paper).