Egalitarianism in Convex Fuzzy Games

R. Brânzei, D.A. Dimitrov, S.H. Tijs

Research output: Working paperDiscussion paperOther research output

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Abstract

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages21
Volume2002-97
Publication statusPublished - 2002

Publication series

NameCentER Discussion Paper
Volume2002-97

Fingerprint

Convex Games
Fuzzy Games
Division
Maximal Element
Cooperative Game
Coalitions
Convexity
Half line
Game
Imply
Arbitrary

Keywords

  • game theory

Cite this

Brânzei, R., Dimitrov, D. A., & Tijs, S. H. (2002). Egalitarianism in Convex Fuzzy Games. (CentER Discussion Paper; Vol. 2002-97). Tilburg: Operations research.
Brânzei, R. ; Dimitrov, D.A. ; Tijs, S.H. / Egalitarianism in Convex Fuzzy Games. Tilburg : Operations research, 2002. (CentER Discussion Paper).
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Brânzei, R, Dimitrov, DA & Tijs, SH 2002 'Egalitarianism in Convex Fuzzy Games' CentER Discussion Paper, vol. 2002-97, Operations research, Tilburg.

Egalitarianism in Convex Fuzzy Games. / Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.

Tilburg : Operations research, 2002. (CentER Discussion Paper; Vol. 2002-97).

Research output: Working paperDiscussion paperOther research output

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N2 - In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.

AB - In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.

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Brânzei R, Dimitrov DA, Tijs SH. Egalitarianism in Convex Fuzzy Games. Tilburg: Operations research. 2002. (CentER Discussion Paper).