A Further Discussion on Cores for Interval-Valued Cooperative Game

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 214)

Abstract

In this paper, we give a further discussion on the core solution for cooperative games with fuzzy payoffs. Some notions and results from classical games are extended to fuzzy cooperative games. Using an example, we point out that the theorem about the nonempty of \(I\)-core proposed in 2008 was not sufficient. Furthermore, the equivalence relation between balanced game and nonempty core, which plays an important role in classic games, does not exist in interval-valued cooperative games. After all, the nonempty of \(I\)-core is proved under the convex situation. It perfects the theory of fuzzy core for interval-valued cooperative game.

Keywords

Cooperative game Interval-valued Core Balanced game 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China and Specialized Research Fund for the Doctoral Program of Higher Education (No. 70771010, 71071018, 70801064, 20111101110036).

References

  1. 1.
    von Neumann J, Morgenstern O (1944) Game theory and economic behavior. Princeton University Press, PrincetonGoogle Scholar
  2. 2.
    Owen G (1995) Game theory, 3rd edn. Academic Press, New YorkGoogle Scholar
  3. 3.
    Tijs S, Branzei R, Ishihara S, Muto S (2004) On cores and stable sets for fuzzy games. Fuzzy Sets Syst 146:285–296MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Mareš M (2001) Fuzzy cooperative games: cooperation with vague expectations. vol 72, Springer, HeidelbergGoogle Scholar
  5. 5.
    Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:183–224Google Scholar
  6. 6.
    Alparslan-Gok S, Miquel S, Tijs S (2009) Cooperation under interval uncertainty. Math Methods Oper Res 69:99–109MathSciNetCrossRefGoogle Scholar
  7. 7.
    Alparslan-Gok S, Branzei R, Tijs S (2009) Cores and stable sets for intervalvalued games. Tilburg UniversityGoogle Scholar
  8. 8.
    Mallozzi L, Scalzo V, Tijs S (2011) Fuzzy interval cooperative games. Fuzzy Sets Syst 165:98–105MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Branzei R, Dimitrov D, Tijs S (2008) Models in cooperative game theory, vol 556. Springer, BerlinGoogle Scholar
  10. 10.
    Klir G, Yuan B (1995) Fuzzy sets and fuzzy logic. Prentice Hall, Upper Saddle RiverGoogle Scholar
  11. 11.
    Gok S, Branzei R, Tijs S (2008) Convex interval gamesGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina

Personalised recommendations