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Fuzzy Information & Engineering and Operations Research & Management pp 409–417Cite as

Fuzzy Average Tree Solution for Graph Games with Fuzzy Coalitions

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 211))

Abstract

In this chapter, the model of graph games with fuzzy coalitions is proposed based on graph games and cooperative games with fuzzy coalitions. The fuzzy average tree solution of graph games with fuzzy coalitions is given, which can be regarded as the generalization of crisp graph games. It is shown that the fuzzy average tree solution is equal to the fuzzy Shapley value for complete graph games with fuzzy coalitions. We extend the notion of link-convexity, under which the fuzzy core is non-empty and the fuzzy average tree solution lies in this core.

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References

  1. Myerson, R.B.: Graphs and cooperation in games. Math. Oper. Res. 2, 225–229 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  2. Borm, P., Owen, G., Tijs, S.H.: On the position value for communication situations. SIAM J. Discrete Math. 5, 305–320 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Meessen, R.: Communication games. University of Nijmegen, Nijmegen, Master thesis (1988)

    Google Scholar 

  4. Slikker, M.: A characterization of the position value. Int. J. Game Theory 33, 505–514 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Herings, P.J.J., Van der Laan, G., Talman, A.J.J.: The average tree solution for cycle-free graph games. Games Econ. Behav. 62, 77–92 (2008)

    Article  MATH  Google Scholar 

  6. Herings, P.J.J., Van der Laan, G., Talman, A.J.J., Yang, Z.: The average tree solution for cooperative games with communication structure. Games Econ. Behav. 68, 626–633 (2010)

    Article  MATH  Google Scholar 

  7. Aubin, J.P.: Mathematical Methods of Game and Economic Theory, Rev edn. North-Holland, Amsterdam (1982)

    Google Scholar 

  8. Butnariu, D.: Stability and Shapley value for n-persons fuzzy game. Fuzzy Sets Syst. 4, 63–72 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tsurumi, M., Tanino, T., Inuiguchi, M.: A Shapley function on a class of cooperative fuzzy games. Eur. J. Oper. Res. 129, 596–618 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tijs, S., Branzei, R., Ishihara, S., Muto, S.: On cores and stable sets for fuzzy games. Fuzzy Sets Syst. 146, 285–296 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yu, X.H., Zhang, Q.: The fuzzy core in games with fuzzy coalitions. J. Comput. Appl. Math. 230, 173–186 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Baron, R., Béal, S., Rémilla, E., Solal, P.: Average tree solutions and the distribution of Harsanyi dividends. Int. J. Game Theory 40, 331–349 (2011)

    Article  MATH  Google Scholar 

  13. Gillies, D.B.: Some Theorems on n-person Games. Princeton University Press, Princeton (1953)

    Google Scholar 

  14. Shapley, L.S.: A value for n-persons games. Ann. Math. Stud. 28, 307–318 (1953)

    MathSciNet  Google Scholar 

  15. Talman, D., Yamamoto, Y.: Average tree solution and subcore for acyclic graph games. J. Oper. Res. Soc. Jpn 51(3), 203–212 (2008)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

Thanks to the support by the National Natural Science Foundation of China (Nos.70771010,71071018, 70801064) and Specialized Research Fund for the Doctoral Program of Higher Education (No. 20111101110036).

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Authors and Affiliations

  1. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Cui-ping Nie & Qiang Zhang

  2. Department of Mathematics and Information Science, Shijiazhuang College, Shijiazhuang, 050035, People’s Republic of China

    Cui-ping Nie

Authors
  1. Cui-ping Nie
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  2. Qiang Zhang
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Corresponding author

Correspondence to Cui-ping Nie .

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Editors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University Higher Education Mega Center, Guangzhou, People's Republic of China

    Bing-Yuan Cao

  2. Department of Mathematics and Computer Sciences, Mazandaran University, Babolsar, Iran

    Hadi Nasseri

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Nie, Cp., Zhang, Q. (2014). Fuzzy Average Tree Solution for Graph Games with Fuzzy Coalitions. In: Cao, BY., Nasseri, H. (eds) Fuzzy Information & Engineering and Operations Research & Management. Advances in Intelligent Systems and Computing, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38667-1_41

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  • DOI: https://doi.org/10.1007/978-3-642-38667-1_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38666-4

  • Online ISBN: 978-3-642-38667-1

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