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Egalitarianism in convex fuzzy games

Author

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  • Branzei,R.
  • Dimitrov,D.

    (Institute of Mathematical Economics, Bielefeld University)

  • Tijs,S.

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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Branzei,R. & Dimitrov,D. & Tijs,S., 2002. "Egalitarianism in convex fuzzy games," Center for Mathematical Economics Working Papers 337, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:337
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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-337.pdf
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    References listed on IDEAS

    as
    1. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 391-399, April.
    2. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Hypercubes and compromise values for cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 155(3), pages 733-740, June.
    3. Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 327-338.
    4. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    5. Klijn, Flip & Slikker, Marco & Tijs, Stef & Zarzuelo, Jose, 2000. "The egalitarian solution for convex games: some characterizations," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 111-121, July.
    6. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    7. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    8. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 147-165.
    9. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    10. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
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    Citations

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    Cited by:

    1. Stef Tijs & Rodica Brânzei, 2004. "Various characterizations of convex fuzzy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 399-408, December.
    2. Yu-Hsien Liao, 2016. "The consistent value for fuzzy games: alternative axiomatizations," Fuzzy Optimization and Decision Making, Springer, vol. 15(2), pages 129-138, June.
    3. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    4. repec:spr:fuzodm:v:16:y:2017:i:3:d:10.1007_s10700-016-9248-6 is not listed on IDEAS
    5. Carles Rafels & Cori Vilella, 2005. "Proportional Share Analysis," Working Papers 218, Barcelona Graduate School of Economics.
    6. Carles Rafels & Cori Vilella, 2007. "Proportional share analysis," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 341-354, December.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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