article

Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games

Authors:

Xiaodong LiuAuthors Info & Claims

Fuzzy Sets and Systems, Volume 188, Issue 1

Pages 88 - 101

https://doi.org/10.1016/j.fss.2011.08.001

Published: 01 February 2012 Publication History

Abstract

Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core.

References

[1]

Aubin, J.P., Cooperative fuzzy games. Mathematics of Operations Research. v6. 1-13.

[2]

Auman, R.J. and Maschler, M., The bargaining sets for cooperative games. In: Dresher, M., Shapley, L.S., Tucker, A.W. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, NJ. pp. 443-476.

[3]

Azrieli, Yaron and Lehrer, Ehud, On some families of cooperative fuzzy games. International Journal of Game Theory. v36. 1-15.

[4]

Branzei, R., Dimitrov, D. and Tijs, S., . 2008. second ed. Springer.

[5]

Butnariu, D. and Kroupa, Toms, Enlarged cores and bargaining schemes in games with fuzzy coalitions. Fuzzy Sets and Systems. v160 i5. 635-643.

[6]

Davis, M. and Maschler, M., Existence of stable payoff configuration for cooperative games. Bulletin of the American Mathematical Society. v69. 106-108.

[7]

Holzman, R., The comparability of the classical and the Mas-Colell bargaining sets. International Journal of Game Theory. v29. 543-553.

[8]

Hwang, Y.A., Fuzzy games: a characterization of the core. Fuzzy Sets and Systems. v158 i22. 2480-2493.

[9]

Husseinov, F., Interpretation of Aubin's fuzzy coalitions and their extensions. Journal of Mathematical Economics. v23. 499-516.

[10]

Mas-Colell, A., An equivalence theorem for a bargaining set. Journal of Mathematical Economics. v18. 129-139.

[11]

Owen, G., . 1995. Academic Press, Inc.

[12]

Peleg, B., Existence theorem for bargaining set M1(i)(v). Bulletin of the American Mathematical Society. v69. 109-110.

[13]

Solymosi, T., On the bargaining set, kernel and core of superadditive games. International Journal of Game Theory. v28. 229-240.

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Vohra, R., An existence theorem for a bargaining set. Journal of Mathematical Economics. v20. 19-34.

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Yang, W., Liu, J. and Liu, X., Aubin Cores and bargaining sets for convex cooperative fuzzy games. International Journal of Game Theory. v40. 467-479.

Cited By

Bai ZChen JZhang X(2024)Triangular Fuzzy Number Intuitionistic Fuzzy Covering Rough Sets and Applications to Decision MakingRough Sets10.1007/978-3-031-65668-2_2(14-28)Online publication date: 17-May-2024
https://dl.acm.org/doi/10.1007/978-3-031-65668-2_2
Yang WLiu JLiu X(2018)Existence of Fuzzy Zhou Bargaining Sets in TU Fuzzy GamesInternational Journal of Fuzzy System Applications10.4018/IJFSA.20180101047:1(46-55)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.4018/IJFSA.2018010104
Yu XZhou HZhang XZhang QLiu YPang J(2017)The fuzzy bargaining set of cooperative game with fuzzy coalitionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-16241733:3(1757-1765)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-162417
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Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games
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Published In

cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 188, Issue 1

February, 2012

102 pages

ISSN:0165-0114

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Copyright © Elsevier B.V. © 2011.

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Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 February 2012

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Cited By

Bai ZChen JZhang X(2024)Triangular Fuzzy Number Intuitionistic Fuzzy Covering Rough Sets and Applications to Decision MakingRough Sets10.1007/978-3-031-65668-2_2(14-28)Online publication date: 17-May-2024
https://dl.acm.org/doi/10.1007/978-3-031-65668-2_2
Yang WLiu JLiu X(2018)Existence of Fuzzy Zhou Bargaining Sets in TU Fuzzy GamesInternational Journal of Fuzzy System Applications10.4018/IJFSA.20180101047:1(46-55)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.4018/IJFSA.2018010104
Yu XZhou HZhang XZhang QLiu YPang J(2017)The fuzzy bargaining set of cooperative game with fuzzy coalitionJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-16241733:3(1757-1765)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-162417
Sun HZhang QWang FYu X(2017)A Fuzzy Owen function on games with coalition structure and fuzzy coalitionsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-16134833:1(159-170)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-161348
Li TMa FLiu W(2013)An approach for obtaining bargaining set in multi-choice gamesProceedings of the 2013 international conference on Integrated Uncertainty in Knowledge Modelling and Decision Making10.1007/978-3-642-39515-4_12(137-148)Online publication date: 12-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39515-4_12

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