# Egalitarianism in Convex Fuzzy Games

R. Brânzei, D.A. Dimitrov, S.H. Tijs

Research output: Working paperDiscussion paperOther research output

### 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 language English Tilburg Operations research 21 2002-97 Published - 2002

### Publication series

Name CentER Discussion Paper 2002-97

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

• 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).
title = "Egalitarianism in Convex Fuzzy Games",
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.",
keywords = "game theory",
author = "R. Br{\^a}nzei and D.A. Dimitrov and S.H. Tijs",
note = "Pagination: 21",
year = "2002",
language = "English",
volume = "2002-97",
series = "CentER Discussion Paper",
publisher = "Operations research",
type = "WorkingPaper",
institution = "Operations research",

}

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

TY - UNPB

T1 - Egalitarianism in Convex Fuzzy Games

AU - Brânzei, R.

AU - Dimitrov, D.A.

AU - Tijs, S.H.

N1 - Pagination: 21

PY - 2002

Y1 - 2002

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.

KW - game theory

M3 - Discussion paper

VL - 2002-97

T3 - CentER Discussion Paper

BT - Egalitarianism in Convex Fuzzy Games

PB - Operations research

CY - Tilburg

ER -

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