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Egalitarianism in convex fuzzy games

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  • Brânzei, R.

    (Tilburg University)

  • Dimitrov, D.A.

    (Tilburg University)

  • Tijs, S.H.

    (Tilburg University)

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.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-140857.

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Date of creation: 2004
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Publication status: Published in Mathematical Social Sciences (2004) v.47, p.313-325
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-140857

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Web page: http://www.tilburguniversity.edu/

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References

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  1. Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer, Springer, vol. 29(3), pages 327-338.
  2. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Hypercubes and Compromise Values for Cooperative Fuzzy Games," Discussion Paper, Tilburg University, Center for Economic Research 2002-14, Tilburg University, Center for Economic Research.
  3. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer, Springer, vol. 30(2), pages 187-193.
  4. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, Springer, vol. 19(2), pages 153-69.
  5. Klijn, F. & Slikker, M. & Tijs, S.H. & Zarzuelo, I., 2000. "The egalitarian solution for convex games: Some characterizations," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-154182, Tilburg University.
  6. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper, Tilburg University, Center for Economic Research 2002-13, Tilburg University, Center for Economic Research.
  7. 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, Springer, vol. 30(2), pages 147-165.
  8. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 615-35, May.
  9. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, Elsevier, vol. 129(3), pages 596-618, March.
  10. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer, Springer, vol. 22(2), pages 391-399, 04.
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Cited by:
  1. Carles Rafels & Cori Vilella, 2005. "Proportional Share Analysis," Working Papers 218, Barcelona Graduate School of Economics.
  2. Carles Rafels & Cori Vilella, 2007. "Proportional share analysis," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 15(2), pages 341-354, December.
  3. 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, Springer, vol. 12(2), pages 399-408, December.

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