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Egalitarianism in convex fuzzy games

  • Branzei, Rodica
  • Dimitrov, Dinko
  • Tijs, Stef

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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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 47 (2004)
Issue (Month): 3 (May)
Pages: 313-325

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Handle: RePEc:eee:matsoc:v:47:y:2004:i:3:p:313-325
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  2. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Hypercubes and Compromise Values for Cooperative Fuzzy Games," Discussion Paper 2002-14, Tilburg University, Center for Economic Research.
  3. 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.
  4. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer, vol. 22(2), pages 391-399, 04.
  5. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003. "Convex fuzzy games and participation monotonic allocation schemes," Other publications TiSEM fbae679e-d7f4-4601-a785-1, Tilburg University, School of Economics and Management.
  6. 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.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-154182 is not listed on IDEAS
  8. repec:ner:tilbur:urn:nbn:nl:ui:12-121813 is not listed on IDEAS
  9. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, vol. 19(2), pages 153-69.
  10. Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer, vol. 29(3), pages 327-338.
  11. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer, vol. 30(2), pages 187-193.
  12. 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, vol. 30(2), pages 147-165.
  13. repec:dgr:kubcen:200214 is not listed on IDEAS
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